Gelfand-Tsetlin Interpretation of Chinta’s A_{5} Polynomial

Ben Brubaker, Daniel Bump, Solomon Friedberg and Jeffrey Hoffstein

October 9, 2005

Pooh-Bah: Mere corroborative detail, intended to lend an air of artistic verisimilitude to an otherwise bald and unconvincing narrative.

–W.S. Gilbert

These computations supplement the proof of Theorem 1.1 in Brubaker, Bump, Friedberg and Hoffstein [1]. There the proof is only sketched; here it is complete.

We quickly restate what is to be proved, referring to [1] for context. In our restatement, p may be taken to be an indeterminant, and if l is even,

g(p^{k}, p^{l}) = \{ \begin{matrix}p^{l} − p^{l−1} & if k ⩾ l > 0, \\ 1 & if l = 0, \\ −p^{k} & if k = l − 1; \\ 0 & otherwise, \end{matrix}

while if l is odd we have

g(p^{k}, p^{l}) = \{ \begin{matrix}p^{k+ \frac{1}{2}} & if k = l − 1; \\ 0 & otherwise . \end{matrix}

By a Gelfand-Tsetlin pattern we mean a pattern

\{ \begin{matrix}λ_{1} & & λ_{2} & & λ_{3} & & ⋯ & & λ_{r} \\ & μ_{1} & & μ_{2} & & ⋯ & & μ_{r−1} \\ & & ν_{1} & & ⋯ & & ν_{r−2} \\ & & & ... & & ... \\ & & & & ρ_{1} \end{matrix}  \}

with r rows, where the entries are integers and the rows interleave; that is, λ_{1} ⩾ μ_{1} ⩾ λ_{2} ⩾ μ_{2} ⩾ ⋯ ⩾ λ_{r}, and μ_{1} ⩾ ν_{1} ⩾ μ_{2} ⩾ ν_{2} ⩾ ⋯ ⩾ ν_{r−1}, etc. We will say that the pattern is strict if each row is strictly increasing, that is, λ_{1} > λ_{2} > λ_{3} > …, μ_{1} > μ_{2} > μ_{3} > …, and so forth.

Let 𝔗 be a strict Gelfand-Tsetlin pattern with top row 5 4 3 2 1 0. There are 7,436 such patterns. We define

G(𝔗) = ∏_{\begin{matrix}i, j ⩾ 1 \\ i + j ⩽ r \end{matrix}} γ(i, j),

where

γ(i, j) = \{ \begin{matrix}g (p^{s+a_{i−1,j}−1}, p^{s+a_{ij}}) & if a_{ij} > a_{i−1,j+1}, \\ p^{s+a_{ij}} & if a_{ij} = a_{i−1,j+1}, \end{matrix}

s = ∑_{k=j+1}^{r−i} a_{ik} − ∑_{k=j+1}^{r−i+1} a_{i−1,k}.

The polynomial that is the numerator given at the end of Chinta [2] is multiplied by (1 + x)(1 + y)(1 + z)(1 + w)(1 + v) and expanded; the coefficient of x^{k_{1}}y^{k_{2}}z^{k_{3}}w^{k_{4}}v^{k_{5}} is denoted h(k_{1}, k_{2}, k_{3}, k_{4}, k_{5}).

Theorem.We have

h(k_{1}, k_{2}, k_{3}, k_{4}, k_{5}) = p^{−(k_{1}+k_{2}+k_{3}+k_{4})/2} ∑ G(𝔗),

where the summation is over all strict Gelfand-Tsetlin patterns

5  4  3  2  1  0
a_{10}  a_{11}  a_{12}  a_{13}  a_{14}
a_{20}  a_{21}  a_{22}  a_{23}
a_{40}  a_{41}  a_{42}
a_{50}  a_{51}
a_{60}

with

∑_{i} a_{1i} − 10 = k_{1},
∑_{i} a_{2i} − 6 = k_{2},
∑_{i} a_{2i} − 3 = k_{3},
∑_{i} a_{4i} − 1 = k_{4},
∑_{i} a_{5i} − 1 = k_{5}.

Proof. There are 1340 values of (k_{1}, k_{2}, k_{3}, k_{4}, k_{5}) with h(k_{1}, k_{2}, k_{3}, k_{4}, k_{5}) ≠ 0.

We list the strict Gelfand-Tsetlin patterns, and for each pattern 𝔗, we list G(𝔗). We group these by (k_{1}, k_{2}, k_{3}, k_{4}, k_{5}) and for each value of (k_{1}, k_{2}, k_{3}, k_{4}, k_{5}), if the sum of the G(𝔗) is nonzero, we match it with one of the terms from the above table. If the sum of the terms exactly cancels, we make not of this. If a table has no annotation, all G(𝔗) vanish for that table.

We find that every value h(k_{1}, k_{2}, k_{3}, k_{4}, k_{5}) is exactly accounted for, as in the following tables.

(0, 0, 0, 0, 0) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 2  1  0 1  0 0  1

h(0, 0, 0, 0, 0) = 1

(0, 0, 0, 0, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 2  1  0 1  0 1  1

h(0, 0, 0, 0, 1) = 1

(0, 0, 0, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 2  1  0 2  0 0  1

h(0, 0, 0, 1, 0) = 1

(0, 0, 0, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 2  1  0 2  0 1 0

(0, 0, 0, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 2  1  0 2  0 2  −1

h(0, 0, 0, 1, 2) = −1

(0, 0, 0, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 2  1  0 2  1 1  −1

h(0, 0, 0, 2, 1) = −1

(0, 0, 0, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 2  1  0 2  1 2  −1

h(0, 0, 0, 2, 2) = −1

(0, 0, 1, 0, 0) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 1  0 0  1

h(0, 0, 1, 0, 0) = 1

(0, 0, 1, 0, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 1  0 1  1

h(0, 0, 1, 0, 1) = 1

(0, 0, 1, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 2  0 0 0

(0, 0, 1, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 2  0 1 0

(0, 0, 1, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 2  0 2 0

(0, 0, 1, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 3  0 0  −1

h(0, 0, 1, 2, 0) = −1

(0, 0, 1, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 2  1 1  (p − 1)

(0, 0, 1, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 3  0 1  0

h(0, 0, 1, 2, 1) = −1 + p

(0, 0, 1, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 2  1 2  (p − 1)

(0, 0, 1, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 3  0 2 −(p − 1)

cancel

(0, 0, 1, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 3  0 3  −p

h(0, 0, 1, 2, 3) = −p

(0, 0, 1, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 3  1 1  p

h(0, 0, 1, 3, 1) = p

(0, 0, 1, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 3  1 2 0

(0, 0, 1, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  1  0 3  1 3  −p

h(0, 0, 1, 3, 3) = −p

h(0, 0, 2, 1, 0) = −1

(0, 0, 2, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 2  0 1 0

(0, 0, 2, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 2  0 2  1

h(0, 0, 2, 1, 2) = 1

(0, 0, 2, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  0 0  −1

h(0, 0, 2, 2, 0) = −1

\begin{matrix}(0, 0, 2, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 2  1 1 & 0 \\ (0, 0, 2, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  0 1 & 0 \end{matrix}

(0, 0, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 2  1 2  0

(0, 0, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  0 2  −(p − 1)

h(0, 0, 2, 2, 2) = 1 − p

(0, 0, 2, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  0 3  −p

h(0, 0, 2, 2, 3) = −p

(0, 0, 2, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  1 1 0

(0, 0, 2, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  1 2 0

(0, 0, 2, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  1 3 0

(0, 0, 2, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  2 2  p

h(0, 0, 2, 4, 2) = p

(0, 0, 2, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  0 3  2 3  p

h(0, 0, 2, 4, 3) = p

(0, 0, 3, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  1 2  1 1  −p

h(0, 0, 3, 2, 1) = −p

h(0, 0, 3, 2, 2) = −p

(0, 0, 3, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  1 3  1 1  −p

h(0, 0, 3, 3, 1) = −p

(0, 0, 3, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  1 3  1 2 0

(0, 0, 3, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  1 3  1 3  p

h(0, 0, 3, 3, 3) = p

(0, 0, 3, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  1 3  2 2  p

h(0, 0, 3, 4, 2) = p

(0, 0, 3, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 3  2  1  0 3  2  1 3  2 3  p

h(0, 0, 3, 4, 3) = p

(0, 1, 0, 0, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 2  1  0 1  0 0  1

h(0, 1, 0, 0, 0) = 1

(0, 1, 0, 0, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 2  1  0 1  0 1  1

h(0, 1, 0, 0, 1) = 1

(0, 1, 0, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 2  1  0 2  0 0  1

h(0, 1, 0, 1, 0) = 1

(0, 1, 0, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 2  1  0 2  0 1 0

(0, 1, 0, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 2  1  0 2  0 2  −1

h(0, 1, 0, 1, 2) = −1

(0, 1, 0, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 2  1  0 2  1 1  −1

h(0, 1, 0, 2, 1) = −1

(0, 1, 0, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 2  1  0 2  1 2  −1

h(0, 1, 0, 2, 2) = −1

(0, 1, 1, 0, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 1  0 0 0

(0, 1, 1, 0, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 1  0 1 0

(0, 1, 1, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 2  0 0 0

(0, 1, 1, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 2  0 1 0

(0, 1, 1, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 2  0 2 0

(0, 1, 1, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 3  0 0 0

\begin{matrix}(0, 1, 1, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 2  1 1 & 0 \\ (0, 1, 1, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(0, 1, 1, 2, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 2  1 2 & 0 \\ (0, 1, 1, 2, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 3  0 2 & 0 \end{matrix}

(0, 1, 1, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 3  0 3 0

(0, 1, 1, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 3  1 1 0

(0, 1, 1, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 3  1 2 0

(0, 1, 1, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  1  0 3  1 3 0

(0, 1, 2, 0, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 1  0 0  −1

h(0, 1, 2, 0, 0) = −1

(0, 1, 2, 0, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 1  0 1  −1

h(0, 1, 2, 0, 1) = −1

(0, 1, 2, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 2  0 0  (p − 1)

(0, 1, 2, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 2  0 0  0

h(0, 1, 2, 1, 0) = −1 + p

\begin{matrix}(0, 1, 2, 1, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 2  0 1 & 0 \\ (0, 1, 2, 1, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 2  0 1 & 0 \end{matrix}
(0, 1, 2, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 2  0 2  −(p − 1)
(0, 1, 2, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 2  0 2  0

h(0, 1, 2, 1, 2) = 1 − p

(0, 1, 2, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 3  0 0  (p − 1)
(0, 1, 2, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 3  0 0 −(p − 1)

cancel

(0, 1, 2, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 2  1 1  0 ; (0, 1, 2, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 3  0 1  0 ; (0, 1, 2, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 2  1 1  −(p − 1) ; (0, 1, 2, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 3  0 1  0 ; h(0, 1, 2, 2, 1) = 1 − p (0, 1, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 2  1 2  0 ; (0, 1, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 3  0 2  (p − 1)^{2} ; (0, 1, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 2  1 2  −(p − 1) ; (0, 1, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 3  0 2  −(p − 1)^{2} ; h(0, 1, 2, 2, 2) = 1 − p

13

(0, 1, 2, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 3  0 3  p(p − 1)

(0, 1, 2, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 3  0 3 −p(p − 1)

cancel

(0, 1, 2, 3, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  0 0  −p

h(0, 1, 2, 3, 0) = −p

\begin{matrix}(0, 1, 2, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 3  1 1 & 0 \\ (0, 1, 2, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 3  1 1 & 0 \\ (0, 1, 2, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  0 1 & 0 \end{matrix}

(0, 1, 2, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 3  1 2  0

(0, 1, 2, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  0 2  −p(p − 1)

h(0, 1, 2, 3, 2) = p − p^{2}

\begin{matrix}(0, 1, 2, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 3  1 3 & 0 \\ (0, 1, 2, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 3  1 3 & 0 \\ (0, 1, 2, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  0 3 & 0 \end{matrix}

(0, 1, 2, 3, 4) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  0 4  p^{2}

h(0, 1, 2, 3, 4) = p^{2}

(0, 1, 2, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  1 1  p

h(0, 1, 2, 4, 1) = p

(0, 1, 2, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 3  2 2  −p(p − 1)

(0, 1, 2, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  1 2  0

h(0, 1, 2, 4, 2) = p − p^{2}

(0, 1, 2, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  0 3  2 3 −p(p − 1)

(0, 1, 2, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  1 3  p(p − 1)

cancel

(0, 1, 2, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  1  0 4  1 4  p^{2}

h(0, 1, 2, 4, 4) = p^{2}

(0, 1, 3, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 2  0 0  p

h(0, 1, 3, 1, 0) = p

(0, 1, 3, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 2  0 1 0

(0, 1, 3, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 2  0 2  −p

h(0, 1, 3, 1, 2) = −p

(0, 1, 3, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  0 0 0

\begin{matrix}(0, 1, 3, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  1 2  1 1 & 0 \\ (0, 1, 3, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 2  1 1 & 0 \\ (0, 1, 3, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(0, 1, 3, 2, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  1 2  1 2 & 0 \\ (0, 1, 3, 2, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 2  1 2 & 0 \\ (0, 1, 3, 2, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  0 2 & 0 \end{matrix}

(0, 1, 3, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  0 3 0

(0, 1, 3, 3, 0) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  0 0  −p

h(0, 1, 3, 3, 0) = −p

\begin{matrix}(0, 1, 3, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  1 3  1 1 & 0 \\ (0, 1, 3, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  1 1 & 0 \\ (0, 1, 3, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  0 1 & 0 \end{matrix}

(0, 1, 3, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  1 3  1 2  0

(0, 1, 3, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  1 2  0

(0, 1, 3, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  0 2  −p(p − 1)

h(0, 1, 3, 3, 2) = p − p^{2}

\begin{matrix}(0, 1, 3, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  1 3  1 3 & 0 \\ (0, 1, 3, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  1 3 & 0 \\ (0, 1, 3, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  0 3 & 0 \end{matrix}

(0, 1, 3, 3, 4) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  0 4  p^{2}

h(0, 1, 3, 3, 4) = p^{2}

(0, 1, 3, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  1 1 0

\begin{matrix}(0, 1, 3, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  1 3  2 2 & 0 \\ (0, 1, 3, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  2 2 & 0 \\ (0, 1, 3, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(0, 1, 3, 4, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 3  2  1 3  2 3 & 0 \\ (0, 1, 3, 4, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 3  2 3 & 0 \\ (0, 1, 3, 4, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  1 3 & 0 \end{matrix}

(0, 1, 3, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  1 4 0

h(0, 1, 3, 5, 2) = p^{2}

(0, 1, 3, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  2 3 0

(0, 1, 3, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  0 4  2 4  −p^{2}

h(0, 1, 3, 5, 4) = −p^{2}

(0, 1, 4, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 2  1 1  p

h(0, 1, 4, 2, 1) = p

(0, 1, 4, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 2  1 2  p

h(0, 1, 4, 2, 2) = p

(0, 1, 4, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 3  1 1 0

(0, 1, 4, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 3  1 2 0

(0, 1, 4, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 3  1 3 0

h(0, 1, 4, 4, 1) = −p

(0, 1, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 3  2 2  p(p − 1)

(0, 1, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 4  1 2  0

h(0, 1, 4, 4, 2) = −p + p^{2}

(0, 1, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 3  2 3  p(p − 1)

(0, 1, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 4  1 3 −p(p − 1)

cancel

(0, 1, 4, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 4  1 4  −p^{2}

h(0, 1, 4, 4, 4) = −p^{2}

(0, 1, 4, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 4  2 2  p^{2}

h(0, 1, 4, 5, 2) = p^{2}

(0, 1, 4, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 4  2 3 0

(0, 1, 4, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  2  1  0 4  2  1 4  2 4  −p^{2}

h(0, 1, 4, 5, 4) = −p^{2}

(0, 2, 1, 0, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 1  0 0  −1

h(0, 2, 1, 0, 0) = −1

(0, 2, 1, 0, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 1  0 1  −1

h(0, 2, 1, 0, 1) = −1

(0, 2, 1, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 2  0 0 0

(0, 2, 1, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 2  0 1 0

(0, 2, 1, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 2  0 2 0

(0, 2, 1, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 3  0 0  1

h(0, 2, 1, 2, 0) = 1

(0, 2, 1, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 2  1 1  −(p − 1)

(0, 2, 1, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 3  0 1  0

h(0, 2, 1, 2, 1) = 1 − p

(0, 2, 1, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 2  1 2 −(p − 1)

(0, 2, 1, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 3  0 2  (p − 1)

cancel

(0, 2, 1, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 3  0 3  p

h(0, 2, 1, 2, 3) = p

(0, 2, 1, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 3  1 1  −p

h(0, 2, 1, 3, 1) = −p

(0, 2, 1, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 3  1 2 0

(0, 2, 1, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  1  0 3  1 3  p

h(0, 2, 1, 3, 3) = p

h(0, 2, 2, 0, 0) = −1

(0, 2, 2, 0, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 1  0 1  −1

h(0, 2, 2, 0, 1) = −1

\begin{matrix}(0, 2, 2, 1, 0) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 2  0 0 & 0 \\ (0, 2, 2, 1, 0) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(0, 2, 2, 1, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 2  0 1 & 0 \\ (0, 2, 2, 1, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(0, 2, 2, 1, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 2  0 2 & 0 \\ (0, 2, 2, 1, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 2  0 2 & 0 \end{matrix}

(0, 2, 2, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  0 0  0 ; (0, 2, 2, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 3  0 0  −(p − 1) ; h(0, 2, 2, 2, 0) = 1 − p (0, 2, 2, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 2  1 1  0 ; (0, 2, 2, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  0 1  0 ; (0, 2, 2, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 2  1 1  −(p − 1) ; (0, 2, 2, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 3  0 1  0 ; h(0, 2, 2, 2, 1) = 1 − p

25

(0, 2, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  0 2  0

(0, 2, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 2  1 2  −(p − 1)

(0, 2, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 3  0 2  −(p − 1)^{2}

h(0, 2, 2, 2, 2) = p − p^{2}

(0, 2, 2, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  0 3  0

(0, 2, 2, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 3  0 3  −p(p − 1)

h(0, 2, 2, 2, 3) = p − p^{2}

(0, 2, 2, 3, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 4  0 0  −p

h(0, 2, 2, 3, 0) = −p

\begin{matrix}(0, 2, 2, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  1 1 & 0 \\ (0, 2, 2, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 3  1 1 & 0 \\ (0, 2, 2, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 4  0 1 & 0 \end{matrix}

(0, 2, 2, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  1 2  0

(0, 2, 2, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 3  1 2  0

(0, 2, 2, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 4  0 2  −p(p − 1)

h(0, 2, 2, 3, 2) = p − p^{2}

\begin{matrix}(0, 2, 2, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  1 3 & 0 \\ (0, 2, 2, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 3  1 3 & 0 \\ (0, 2, 2, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 4  0 3 & 0 \end{matrix}

h(0, 2, 2, 3, 4) = p^{2}

(0, 2, 2, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 4  1 1  p

h(0, 2, 2, 4, 1) = p

\begin{matrix}(0, 2, 2, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  2 2 & 0 \\ (0, 2, 2, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 4  1 2 & 0 \end{matrix}

(0, 2, 2, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  0 3  2 3  0

(0, 2, 2, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 4  1 3  p(p − 1)

h(0, 2, 2, 4, 3) = −p + p^{2}

(0, 2, 2, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  1  0 4  1 4  p^{2}

h(0, 2, 2, 4, 4) = p^{2}

(0, 2, 3, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 2  0 0 0

(0, 2, 3, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 2  0 1 0

(0, 2, 3, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 2  0 2 0

(0, 2, 3, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  0 0 0

(0, 2, 3, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  1 2  1 1  −p(p − 1)

(0, 2, 3, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 2  1 1  0

(0, 2, 3, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  0 1  0

h(0, 2, 3, 2, 1) = p − p^{2}

(0, 2, 3, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 2  1 2  0

(0, 2, 3, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  0 2  0

h(0, 2, 3, 2, 2) = p − p^{2}

(0, 2, 3, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  0 3 0

(0, 2, 3, 3, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  0 0 0

(0, 2, 3, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  1 3  1 1  −p(p − 1)

(0, 2, 3, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  1 1  0

(0, 2, 3, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  0 1  0

h(0, 2, 3, 3, 1) = p − p^{2}

\begin{matrix}(0, 2, 3, 3, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  1 3  1 2 & 0 \\ (0, 2, 3, 3, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  1 2 & 0 \\ (0, 2, 3, 3, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  0 2 & 0 \end{matrix}

(0, 2, 3, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  1 3  1 3  p(p − 1)

(0, 2, 3, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  1 3  0

(0, 2, 3, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  0 3  0

h(0, 2, 3, 3, 3) = −p + p^{2}

(0, 2, 3, 3, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  0 4 0

(0, 2, 3, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  1 1 0

(0, 2, 3, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  2 2  0

(0, 2, 3, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  1 2  0

h(0, 2, 3, 4, 2) = −p + p^{2}

(0, 2, 3, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 3  2  1 3  2 3  p(p − 1)

(0, 2, 3, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 3  2 3  0

(0, 2, 3, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  1 3  0

h(0, 2, 3, 4, 3) = −p + p^{2}

(0, 2, 3, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  1 4 0

(0, 2, 3, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  2 2 0

(0, 2, 3, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  2 3 0

(0, 2, 3, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  0 4  2 4 0

(0, 2, 4, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  0 0  p

h(0, 2, 4, 2, 0) = p

(0, 2, 4, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 2  1 1  −p(p − 1)

(0, 2, 4, 2, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  0 1  0

h(0, 2, 4, 2, 1) = p − p^{2}

(0, 2, 4, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 2  1 2 −p(p − 1)

(0, 2, 4, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  0 2  p(p − 1)

cancel

(0, 2, 4, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  0 3  p^{2}

h(0, 2, 4, 2, 3) = p^{2}

(0, 2, 4, 3, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  0 0  p

h(0, 2, 4, 3, 0) = p

\begin{matrix}(0, 2, 4, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 3  1 1 & 0 \\ (0, 2, 4, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  1 1 & 0 \\ (0, 2, 4, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  0 1 & 0 \end{matrix}

(0, 2, 4, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 3  1 2  0

(0, 2, 4, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  1 2  0

(0, 2, 4, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  0 2  p(p − 1)

h(0, 2, 4, 3, 2) = −p + p^{2}

\begin{matrix}(0, 2, 4, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 3  1 3 & 0 \\ (0, 2, 4, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  1 3 & 0 \\ (0, 2, 4, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  0 3 & 0 \end{matrix}

(0, 2, 4, 3, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  0 4  −p^{2}

h(0, 2, 4, 3, 4) = −p^{2}

(0, 2, 4, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 4  1 1  p(p − 1)

(0, 2, 4, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  1 1  0

h(0, 2, 4, 4, 1) = −p + p^{2}

(0, 2, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 3  2 2  −p(p − 1)^{2} ; (0, 2, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 4  1 2  0 ; (0, 2, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  2 2  p^{2}(p − 1) ; (0, 2, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  1 2  0 ; h(0, 2, 4, 4, 2) = −p + p^{2} (0, 2, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 3  2 3  −p(p − 1)^{2} ; (0, 2, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 4  1 3  p(p − 1)^{2} ; (0, 2, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 3  2 3  p^{2}(p − 1) ; (0, 2, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  1 3  0 ; h(0, 2, 4, 4, 3) = −p^{2} + p^{3}

36

(0, 2, 4, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 4  1 4  p^{2}(p − 1)
(0, 2, 4, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  1 4  0

h(0, 2, 4, 4, 4) = −p^{2} + p^{3}

(0, 2, 4, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 4  2 2 −p^{2}(p − 1)
(0, 2, 4, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  2 2  p^{2}(p − 1)

cancel

\begin{matrix}(0, 2, 4, 5, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 4  2 3 & 0 \\ (0, 2, 4, 5, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  2 3 & 0 \end{matrix}
(0, 2, 4, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  2  1 4  2 4  p^{2}(p − 1)
(0, 2, 4, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  2 4 −p^{2}(p − 1)

cancel

h(0, 2, 4, 6, 3) = −p^{3}

(0, 2, 4, 6, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  0 4  3 4  −p^{3}

h(0, 2, 4, 6, 4) = −p^{3}

(0, 2, 5, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 3  1 1  p^{2}

h(0, 2, 5, 3, 1) = p^{2}

(0, 2, 5, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 3  1 2 0

(0, 2, 5, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 3  1 3  −p^{2}

h(0, 2, 5, 3, 3) = −p^{2}

(0, 2, 5, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 4  1 1  p^{2}

h(0, 2, 5, 4, 1) = p^{2}

\begin{matrix}(0, 2, 5, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 3  2 2 & 0 \\ (0, 2, 5, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 4  1 2 & 0 \end{matrix}

(0, 2, 5, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 3  2 3  0

(0, 2, 5, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 4  1 3  p^{2}(p − 1)

h(0, 2, 5, 4, 3) = −p^{2} + p^{3}

(0, 2, 5, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 4  1 4  p^{3}

h(0, 2, 5, 4, 4) = p^{3}

(0, 2, 5, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 4  2 2 0

(0, 2, 5, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 4  2 3 0

(0, 2, 5, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 4  2 4 0

h(0, 2, 5, 6, 3) = −p^{3}

(0, 2, 5, 6, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  1  0 4  3  1 4  3 4  −p^{3}

h(0, 2, 5, 6, 4) = −p^{3}

(0, 3, 2, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 2  0 0  −p

h(0, 3, 2, 1, 0) = −p

(0, 3, 2, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 2  0 1 0

(0, 3, 2, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 2  0 2  p

h(0, 3, 2, 1, 2) = p

(0, 3, 2, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 3  0 0  −p

h(0, 3, 2, 2, 0) = −p

\begin{matrix}(0, 3, 2, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 2  1 1 & 0 \\ (0, 3, 2, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 3  0 1 & 0 \end{matrix}

(0, 3, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 2  1 2  0

(0, 3, 2, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 3  0 2  −p(p − 1)

h(0, 3, 2, 2, 2) = p − p^{2}

(0, 3, 2, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 3  0 3  −p^{2}

h(0, 3, 2, 2, 3) = −p^{2}

(0, 3, 2, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 3  1 1 0

(0, 3, 2, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 3  1 2 0

(0, 3, 2, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 3  1 3 0

h(0, 3, 2, 4, 2) = p^{2}

(0, 3, 2, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  0 3  2 3  p^{2}

h(0, 3, 2, 4, 3) = p^{2}

(0, 3, 3, 1, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 2  0 0  −p

h(0, 3, 3, 1, 0) = −p

(0, 3, 3, 1, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 2  0 1 0

(0, 3, 3, 1, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 2  0 2  p

h(0, 3, 3, 1, 2) = p

(0, 3, 3, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  0 0 0

\begin{matrix}(0, 3, 3, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  1 2  1 1 & 0 \\ (0, 3, 3, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 2  1 1 & 0 \\ (0, 3, 3, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(0, 3, 3, 2, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  1 2  1 2 & 0 \\ (0, 3, 3, 2, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 2  1 2 & 0 \\ (0, 3, 3, 2, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  0 2 & 0 \end{matrix}

(0, 3, 3, 2, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  0 3 0

(0, 3, 3, 3, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  0 0  p

h(0, 3, 3, 3, 0) = p

\begin{matrix}(0, 3, 3, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  1 3  1 1 & 0 \\ (0, 3, 3, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  1 1 & 0 \\ (0, 3, 3, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  0 1 & 0 \end{matrix}

(0, 3, 3, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  1 3  1 2  0

(0, 3, 3, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  1 2  0

(0, 3, 3, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  0 2  p(p − 1)

h(0, 3, 3, 3, 2) = −p + p^{2}

\begin{matrix}(0, 3, 3, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  1 3  1 3 & 0 \\ (0, 3, 3, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  1 3 & 0 \\ (0, 3, 3, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  0 3 & 0 \end{matrix}

h(0, 3, 3, 3, 4) = −p^{2}

(0, 3, 3, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  1 1 0

\begin{matrix}(0, 3, 3, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  1 3  2 2 & 0 \\ (0, 3, 3, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  2 2 & 0 \\ (0, 3, 3, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(0, 3, 3, 4, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 3  2  1 3  2 3 & 0 \\ (0, 3, 3, 4, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 3  2 3 & 0 \\ (0, 3, 3, 4, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  1 3 & 0 \end{matrix}

(0, 3, 3, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  1 4 0

h(0, 3, 3, 5, 2) = −p^{2}

(0, 3, 3, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  2 3 0

(0, 3, 3, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  0 4  2 4  p^{2}

h(0, 3, 3, 5, 4) = p^{2}

(0, 3, 4, 2, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 3  0 0  p

h(0, 3, 4, 2, 0) = p

\begin{matrix}(0, 3, 4, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 2  1 1 & 0 \\ (0, 3, 4, 2, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 3  0 1 & 0 \end{matrix}

(0, 3, 4, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 2  1 2  0

(0, 3, 4, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 3  0 2  p(p − 1)

h(0, 3, 4, 2, 2) = −p + p^{2}

h(0, 3, 4, 2, 3) = p^{2}

(0, 3, 4, 3, 0) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  0 0  p

h(0, 3, 4, 3, 0) = p

\begin{matrix}(0, 3, 4, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 3  1 1 & 0 \\ (0, 3, 4, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 3  1 1 & 0 \\ (0, 3, 4, 3, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  0 1 & 0 \end{matrix}

(0, 3, 4, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 3  1 2  0

(0, 3, 4, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 3  1 2  0

(0, 3, 4, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  0 2  p(p − 1)

h(0, 3, 4, 3, 2) = −p + p^{2}

\begin{matrix}(0, 3, 4, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 3  1 3 & 0 \\ (0, 3, 4, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 3  1 3 & 0 \\ (0, 3, 4, 3, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  0 3 & 0 \end{matrix}

(0, 3, 4, 3, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  0 4  −p^{2}

h(0, 3, 4, 3, 4) = −p^{2}

\begin{matrix}(0, 3, 4, 4, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 4  1 1 & 0 \\ (0, 3, 4, 4, 1) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  1 1 & 0 \end{matrix}

(0, 3, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 3  2 2  0 ; (0, 3, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 4  1 2  0 ; (0, 3, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 3  2 2  p^{2}(p − 1) ; (0, 3, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  1 2  0 ; h(0, 3, 4, 4, 2) = −p^{2} + p^{3} (0, 3, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 3  2 3  0 ; (0, 3, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 4  1 3  0 ; (0, 3, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 3  2 3  p^{2}(p − 1) ; (0, 3, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  1 3  0 ; h(0, 3, 4, 4, 3) = −p^{2} + p^{3}

49

\begin{matrix}(0, 3, 4, 4, 4) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 4  1 4 & 0 \\ (0, 3, 4, 4, 4) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  1 4 & 0 \end{matrix}

(0, 3, 4, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 4  2 2  0

(0, 3, 4, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  2 2  p^{2}(p − 1)

h(0, 3, 4, 5, 2) = −p^{2} + p^{3}

\begin{matrix}(0, 3, 4, 5, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 4  2 3 & 0 \\ (0, 3, 4, 5, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  2 3 & 0 \end{matrix}

(0, 3, 4, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  2  1 4  2 4  0

(0, 3, 4, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  2 4  −p^{2}(p − 1)

h(0, 3, 4, 5, 4) = p^{2} − p^{3}

h(0, 3, 4, 6, 3) = −p^{3}

(0, 3, 4, 6, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  0 4  3 4  −p^{3}

h(0, 3, 4, 6, 4) = −p^{3}

(0, 3, 5, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 3  1 1 0

(0, 3, 5, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 3  1 2 0

(0, 3, 5, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 3  1 3 0

(0, 3, 5, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  1 1 0

\begin{matrix}(0, 3, 5, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 3  2 2 & 0 \\ (0, 3, 5, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(0, 3, 5, 4, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 3  2 3 & 0 \\ (0, 3, 5, 4, 3) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  1 3 & 0 \end{matrix}

(0, 3, 5, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  1 4 0

(0, 3, 5, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  2 2 0

(0, 3, 5, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  2 3 0

(0, 3, 5, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  2 4 0

(0, 3, 5, 6, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  3 3 0

(0, 3, 5, 6, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  1 4  3 4 0

h(0, 3, 6, 4, 2) = −p^{3}

(0, 3, 6, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  2 3  2 3  −p^{3}

h(0, 3, 6, 4, 3) = −p^{3}

(0, 3, 6, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  2 4  2 2  −p^{3}

h(0, 3, 6, 5, 2) = −p^{3}

(0, 3, 6, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  2 4  2 3 0

(0, 3, 6, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  2 4  2 4  p^{3}

h(0, 3, 6, 5, 4) = p^{3}

(0, 3, 6, 6, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  2 4  3 3  p^{3}

h(0, 3, 6, 6, 3) = p^{3}

(0, 3, 6, 6, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  0 4  3  2 4  3 4  p^{3}

h(0, 3, 6, 6, 4) = p^{3}

h(0, 4, 3, 2, 1) = p^{2}

(0, 4, 3, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 3  2  1 2  1 2  p^{2}

h(0, 4, 3, 2, 2) = p^{2}

(0, 4, 3, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 3  2  1 3  1 1  p^{2}

h(0, 4, 3, 3, 1) = p^{2}

(0, 4, 3, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 3  2  1 3  1 2 0

(0, 4, 3, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 3  2  1 3  1 3  −p^{2}

h(0, 4, 3, 3, 3) = −p^{2}

(0, 4, 3, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 3  2  1 3  2 2  −p^{2}

h(0, 4, 3, 4, 2) = −p^{2}

(0, 4, 3, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 3  2  1 3  2 3  −p^{2}

h(0, 4, 3, 4, 3) = −p^{2}

h(0, 4, 4, 2, 1) = p^{2}

(0, 4, 4, 2, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 2  1 2  p^{2}

h(0, 4, 4, 2, 2) = p^{2}

(0, 4, 4, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 3  1 1 0

(0, 4, 4, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 3  1 2 0

(0, 4, 4, 3, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 3  1 3 0

(0, 4, 4, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 4  1 1  −p^{2}

h(0, 4, 4, 4, 1) = −p^{2}

(0, 4, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 3  2 2  p^{2}(p − 1)

(0, 4, 4, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 4  1 2  0

h(0, 4, 4, 4, 2) = −p^{2} + p^{3}

(0, 4, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 3  2 3  p^{2}(p − 1)

(0, 4, 4, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 4  1 3 −p^{2}(p − 1)

cancel

(0, 4, 4, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 4  1 4  −p^{3}

h(0, 4, 4, 4, 4) = −p^{3}

(0, 4, 4, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 4  2 2  p^{3}

h(0, 4, 4, 5, 2) = p^{3}

(0, 4, 4, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 4  2 3 0

(0, 4, 4, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  2  1 4  2 4  −p^{3}

h(0, 4, 4, 5, 4) = −p^{3}

(0, 4, 5, 3, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 3  1 1  −p^{2}

h(0, 4, 5, 3, 1) = −p^{2}

(0, 4, 5, 3, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 3  1 2 0

h(0, 4, 5, 3, 3) = p^{2}

(0, 4, 5, 4, 1) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  1 1  −p^{2}

h(0, 4, 5, 4, 1) = −p^{2}

\begin{matrix}(0, 4, 5, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 3  2 2 & 0 \\ (0, 4, 5, 4, 2) & 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  1 2 & 0 \end{matrix}

(0, 4, 5, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 3  2 3  0

(0, 4, 5, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  1 3  −p^{2}(p − 1)

h(0, 4, 5, 4, 3) = p^{2} − p^{3}

(0, 4, 5, 4, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  1 4  −p^{3}

h(0, 4, 5, 4, 4) = −p^{3}

(0, 4, 5, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  2 2 0

(0, 4, 5, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  2 3 0

(0, 4, 5, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  2 4 0

(0, 4, 5, 6, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  3 3  p^{3}

h(0, 4, 5, 6, 3) = p^{3}

(0, 4, 5, 6, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  1 4  3 4  p^{3}

h(0, 4, 5, 6, 4) = p^{3}

(0, 4, 6, 4, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  2 3  2 2  −p^{3}

h(0, 4, 6, 4, 2) = −p^{3}

(0, 4, 6, 4, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  2 3  2 3  −p^{3}

h(0, 4, 6, 4, 3) = −p^{3}

(0, 4, 6, 5, 2) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  2 4  2 2  −p^{3}

h(0, 4, 6, 5, 2) = −p^{3}

(0, 4, 6, 5, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  2 4  2 3 0

(0, 4, 6, 5, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  2 4  2 4  p^{3}

h(0, 4, 6, 5, 4) = p^{3}

(0, 4, 6, 6, 3) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  2 4  3 3  p^{3}

h(0, 4, 6, 6, 3) = p^{3}

(0, 4, 6, 6, 4) 5  4  3  2  1  0 4  3  2  1  0 4  3  2  1 4  3  2 4  3 4  p^{3}

h(0, 4, 6, 6, 4) = p^{3}

(1, 0, 0, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 2  1  0 1  0 0  1

h(1, 0, 0, 0, 0) = 1

(1, 0, 0, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 2  1  0 1  0 1  1

h(1, 0, 0, 0, 1) = 1

(1, 0, 0, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 2  1  0 2  0 0  1

h(1, 0, 0, 1, 0) = 1

(1, 0, 0, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 2  1  0 2  0 1 0

(1, 0, 0, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 2  1  0 2  0 2  −1

h(1, 0, 0, 1, 2) = −1

(1, 0, 0, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 2  1  0 2  1 1  −1

h(1, 0, 0, 2, 1) = −1

(1, 0, 0, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 2  1  0 2  1 2  −1

h(1, 0, 0, 2, 2) = −1

(1, 0, 1, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 1  0 0  1

h(1, 0, 1, 0, 0) = 1

(1, 0, 1, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 1  0 1  1

h(1, 0, 1, 0, 1) = 1

(1, 0, 1, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 2  0 0 0

(1, 0, 1, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 2  0 1 0

(1, 0, 1, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 2  0 2 0

(1, 0, 1, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 3  0 0  −1

h(1, 0, 1, 2, 0) = −1

(1, 0, 1, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 2  1 1  (p − 1)

(1, 0, 1, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 3  0 1  0

h(1, 0, 1, 2, 1) = −1 + p

(1, 0, 1, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 2  1 2  (p − 1)

(1, 0, 1, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 3  0 2 −(p − 1)

cancel

(1, 0, 1, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 3  0 3  −p

h(1, 0, 1, 2, 3) = −p

h(1, 0, 1, 3, 1) = p

(1, 0, 1, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 3  1 2 0

(1, 0, 1, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  1  0 3  1 3  −p

h(1, 0, 1, 3, 3) = −p

(1, 0, 2, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 2  0 0  −1

h(1, 0, 2, 1, 0) = −1

(1, 0, 2, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 2  0 1 0

(1, 0, 2, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 2  0 2  1

h(1, 0, 2, 1, 2) = 1

(1, 0, 2, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 3  0 0  −1

h(1, 0, 2, 2, 0) = −1

\begin{matrix}(1, 0, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 2  1 1 & 0 \\ (1, 0, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 3  0 1 & 0 \end{matrix}

(1, 0, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 2  1 2  0

(1, 0, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 3  0 2  −(p − 1)

h(1, 0, 2, 2, 2) = 1 − p

(1, 0, 2, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 3  0 3  −p

h(1, 0, 2, 2, 3) = −p

(1, 0, 2, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 3  1 1 0

(1, 0, 2, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 3  1 2 0

(1, 0, 2, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 3  1 3 0

h(1, 0, 2, 4, 2) = p

(1, 0, 2, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  0 3  2 3  p

h(1, 0, 2, 4, 3) = p

(1, 0, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  1 2  1 1  −p

h(1, 0, 3, 2, 1) = −p

(1, 0, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  1 2  1 2  −p

h(1, 0, 3, 2, 2) = −p

(1, 0, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  1 3  1 1  −p

h(1, 0, 3, 3, 1) = −p

(1, 0, 3, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  1 3  1 2 0

(1, 0, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  1 3  1 3  p

h(1, 0, 3, 3, 3) = p

h(1, 0, 3, 4, 2) = p

(1, 0, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 3  2  1  0 3  2  1 3  2 3  p

h(1, 0, 3, 4, 3) = p

(1, 1, 0, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 2  1  0 1  0 0 0

(1, 1, 0, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 2  1  0 1  0 1 0

(1, 1, 0, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 2  1  0 2  0 0 0

(1, 1, 0, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 2  1  0 2  0 1 0

(1, 1, 0, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 2  1  0 2  0 2 0

(1, 1, 0, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 2  1  0 2  1 1 0

(1, 1, 0, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 2  1  0 2  1 2 0

(1, 1, 1, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 1  0 0 0

(1, 1, 1, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 1  0 1 0

(1, 1, 1, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 2  0 0 0

(1, 1, 1, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 2  0 1 0

(1, 1, 1, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 2  0 2 0

(1, 1, 1, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 3  0 0 0

\begin{matrix}(1, 1, 1, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 2  1 1 & 0 \\ (1, 1, 1, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(1, 1, 1, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 2  1 2 & 0 \\ (1, 1, 1, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 3  0 2 & 0 \end{matrix}

(1, 1, 1, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 3  0 3 0

(1, 1, 1, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 3  1 1 0

(1, 1, 1, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 3  1 2 0

(1, 1, 1, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  1  0 3  1 3 0

(1, 1, 2, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 1  0 0 0

(1, 1, 2, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 1  0 1 0

\begin{matrix}(1, 1, 2, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 2  0 0 & 0 \\ (1, 1, 2, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(1, 1, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 2  0 1 & 0 \\ (1, 1, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(1, 1, 2, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 2  0 2 & 0 \\ (1, 1, 2, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 2  0 2 & 0 \end{matrix}

\begin{matrix}(1, 1, 2, 2, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  0 0 & 0 \\ (1, 1, 2, 2, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 3  0 0 & 0 \end{matrix}

\begin{matrix}(1, 1, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 2  1 1 & 0 \\ (1, 1, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  0 1 & 0 \\ (1, 1, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 2  1 1 & 0 \\ (1, 1, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 3  0 1 & 0 \end{matrix} \begin{matrix}(1, 1, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 2  1 2 & 0 \\ (1, 1, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  0 2 & 0 \\ (1, 1, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 2  1 2 & 0 \\ (1, 1, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 3  0 2 & 0 \end{matrix}

69

\begin{matrix}(1, 1, 2, 2, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  0 3 & 0 \\ (1, 1, 2, 2, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 3  0 3 & 0 \end{matrix}

(1, 1, 2, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  0 0 0

\begin{matrix}(1, 1, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  1 1 & 0 \\ (1, 1, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 3  1 1 & 0 \\ (1, 1, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  0 1 & 0 \end{matrix}

\begin{matrix}(1, 1, 2, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  1 2 & 0 \\ (1, 1, 2, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 3  1 2 & 0 \\ (1, 1, 2, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  0 2 & 0 \end{matrix}

\begin{matrix}(1, 1, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  1 3 & 0 \\ (1, 1, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 3  1 3 & 0 \\ (1, 1, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  0 3 & 0 \end{matrix}

(1, 1, 2, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  0 4 0

(1, 1, 2, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  1 1 0

\begin{matrix}(1, 1, 2, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  2 2 & 0 \\ (1, 1, 2, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(1, 1, 2, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  0 3  2 3 & 0 \\ (1, 1, 2, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  1 3 & 0 \end{matrix}

(1, 1, 2, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  1  0 4  1 4 0

(1, 1, 3, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 2  0 0 0

(1, 1, 3, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 2  0 1 0

(1, 1, 3, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 2  0 2 0

(1, 1, 3, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  0 0 0

\begin{matrix}(1, 1, 3, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  1 2  1 1 & 0 \\ (1, 1, 3, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 2  1 1 & 0 \\ (1, 1, 3, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(1, 1, 3, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  1 2  1 2 & 0 \\ (1, 1, 3, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 2  1 2 & 0 \\ (1, 1, 3, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  0 2 & 0 \end{matrix}

(1, 1, 3, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  0 3 0

(1, 1, 3, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  0 0 0

\begin{matrix}(1, 1, 3, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  1 3  1 1 & 0 \\ (1, 1, 3, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  1 1 & 0 \\ (1, 1, 3, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  0 1 & 0 \end{matrix}

\begin{matrix}(1, 1, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  1 3  1 2 & 0 \\ (1, 1, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  1 2 & 0 \\ (1, 1, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  0 2 & 0 \end{matrix}

\begin{matrix}(1, 1, 3, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  1 3  1 3 & 0 \\ (1, 1, 3, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  1 3 & 0 \\ (1, 1, 3, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  0 3 & 0 \end{matrix}

(1, 1, 3, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  0 4 0

(1, 1, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  1 1 0

\begin{matrix}(1, 1, 3, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  1 3  2 2 & 0 \\ (1, 1, 3, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  2 2 & 0 \\ (1, 1, 3, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(1, 1, 3, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 3  2  1 3  2 3 & 0 \\ (1, 1, 3, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 3  2 3 & 0 \\ (1, 1, 3, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  1 3 & 0 \end{matrix}

(1, 1, 3, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  1 4 0

(1, 1, 3, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  2 2 0

(1, 1, 3, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  2 3 0

(1, 1, 3, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  0 4  2 4 0

(1, 1, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 2  1 1 0

(1, 1, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 2  1 2 0

(1, 1, 4, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 3  1 1 0

(1, 1, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 3  1 2 0

(1, 1, 4, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 3  1 3 0

(1, 1, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 4  1 1 0

\begin{matrix}(1, 1, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 3  2 2 & 0 \\ (1, 1, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(1, 1, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 3  2 3 & 0 \\ (1, 1, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 4  1 3 & 0 \end{matrix}

(1, 1, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 4  1 4 0

(1, 1, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 4  2 2 0

(1, 1, 4, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 4  2 3 0

(1, 1, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 4  2  1  0 4  2  1 4  2 4 0

(1, 2, 0, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 2  1  0 1  0 0  −1

h(1, 2, 0, 0, 0) = −1

(1, 2, 0, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 2  1  0 1  0 1  −1

h(1, 2, 0, 0, 1) = −1

h(1, 2, 0, 1, 0) = −1

(1, 2, 0, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 2  1  0 2  0 1 0

(1, 2, 0, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 2  1  0 2  0 2  1

h(1, 2, 0, 1, 2) = 1

(1, 2, 0, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 2  1  0 2  1 1  1

h(1, 2, 0, 2, 1) = 1

(1, 2, 0, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 2  1  0 2  1 2  1

h(1, 2, 0, 2, 2) = 1

(1, 2, 1, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 1  0 0  (p − 1)

(1, 2, 1, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 1  0 0  0

h(1, 2, 1, 0, 0) = −1 + p

(1, 2, 1, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 1  0 1  (p − 1)

(1, 2, 1, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 1  0 1  0

h(1, 2, 1, 0, 1) = −1 + p

\begin{matrix}(1, 2, 1, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 2  0 0 & 0 \\ (1, 2, 1, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(1, 2, 1, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 2  0 1 & 0 \\ (1, 2, 1, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(1, 2, 1, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 2  0 2 & 0 \\ (1, 2, 1, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 2  0 2 & 0 \end{matrix}

(1, 2, 1, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 3  0 0  −(p − 1) ; (1, 2, 1, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 3  0 0  0 ; h(1, 2, 1, 2, 0) = 1 − p (1, 2, 1, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 2  1 1  (p − 1)^{2} ; (1, 2, 1, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 3  0 1  0 ; (1, 2, 1, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 2  1 1  0 ; (1, 2, 1, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 3  0 1  0 ; h(1, 2, 1, 2, 1) = 1 − 2p + p^{2}

80

(1, 2, 1, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 2  1 2  (p − 1)^{2}

(1, 2, 1, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 3  0 2 −(p − 1)^{2}

(1, 2, 1, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 2  1 2  0

(1, 2, 1, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 3  0 2  0

cancel

(1, 2, 1, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 3  0 3  −p(p − 1)

(1, 2, 1, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 3  0 3  0

h(1, 2, 1, 2, 3) = p − p^{2}

(1, 2, 1, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 3  1 1  p(p − 1)

(1, 2, 1, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 3  1 1  0

h(1, 2, 1, 3, 1) = −p + p^{2}

\begin{matrix}(1, 2, 1, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 3  1 2 & 0 \\ (1, 2, 1, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 3  1 2 & 0 \end{matrix}
(1, 2, 1, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  1  0 3  1 3  −p(p − 1)
(1, 2, 1, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  1  0 3  1 3  0

h(1, 2, 1, 3, 3) = p − p^{2}

(1, 2, 2, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 1  0 0  (p − 1)
(1, 2, 2, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 1  0 0 −(p − 1)

cancel

(1, 2, 2, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 1  0 1  (p − 1)
(1, 2, 2, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 1  0 1 −(p − 1)

cancel

(1, 2, 2, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 2  0 0  0 ; (1, 2, 2, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 2  0 0  0 ; (1, 2, 2, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 2  0 0  −(p − 1) ; (1, 2, 2, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 2  0 0  0 ; h(1, 2, 2, 1, 0) = 1 − p \begin{matrix}(1, 2, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 2  0 1 & 0 \\ (1, 2, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 2  0 1 & 0 \\ (1, 2, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 2  0 1 & 0 \\ (1, 2, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 2  0 1 & 0 \end{matrix}

83

(1, 2, 2, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 2  0 2  0 ; (1, 2, 2, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 2  0 2  0 ; (1, 2, 2, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 2  0 2  (p − 1) ; (1, 2, 2, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 2  0 2  0 ; h(1, 2, 2, 1, 2) = −1 + p (1, 2, 2, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 3  0 0  0 ; (1, 2, 2, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 3  0 0  (p − 1)^{2} ; (1, 2, 2, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  0 0  −(p − 1) ; (1, 2, 2, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 3  0 0  −(p − 1)^{2} ; h(1, 2, 2, 2, 0) = 1 − p

84

(1, 2, 2, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 2  1 1  0
(1, 2, 2, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 3  0 1  0
(1, 2, 2, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 2  1 1  (p − 1)^{2}
(1, 2, 2, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 3  0 1  0
(1, 2, 2, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 2  1 1  0
(1, 2, 2, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  0 1  0
(1, 2, 2, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 2  1 1 −(p − 1)^{2}
(1, 2, 2, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 3  0 1  0

cancel

(1, 2, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 3  0 2  0

(1, 2, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 2  1 2  (p − 1)^{2}

(1, 2, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 3  0 2  (p − 1)^{3}

(1, 2, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 2  1 2  0

(1, 2, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  0 2  −(p − 1)^{2}

(1, 2, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 2  1 2  −(p − 1)^{2}

(1, 2, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 3  0 2  −(p − 1)^{3}

h(1, 2, 2, 2, 2) = −1 + 2p − p^{2}

(1, 2, 2, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 3  0 3  0 ; (1, 2, 2, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 3  0 3  p(p − 1)^{2} ; (1, 2, 2, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  0 3  −p(p − 1) ; (1, 2, 2, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 3  0 3  −p(p − 1)^{2} ; h(1, 2, 2, 2, 3) = p − p^{2} (1, 2, 2, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  0 0  p(p − 1) ; (1, 2, 2, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  0 0 −p(p − 1) ; cancel

87

\begin{matrix}(1, 2, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 3  1 1 & 0 \\ (1, 2, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 3  1 1 & 0 \\ (1, 2, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  0 1 & 0 \\ (1, 2, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  1 1 & 0 \\ (1, 2, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 3  1 1 & 0 \\ (1, 2, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  0 1 & 0 \end{matrix}

88

(1, 2, 2, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 3  1 2  0
(1, 2, 2, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 3  1 2  0
(1, 2, 2, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  0 2  p(p − 1)^{2}
(1, 2, 2, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  1 2  0
(1, 2, 2, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 3  1 2  0
(1, 2, 2, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  0 2 −p(p − 1)^{2}

cancel

\begin{matrix}(1, 2, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 3  1 3 & 0 \\ (1, 2, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 3  1 3 & 0 \\ (1, 2, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  0 3 & 0 \\ (1, 2, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  1 3 & 0 \\ (1, 2, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 3  1 3 & 0 \\ (1, 2, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  0 3 & 0 \end{matrix} (1, 2, 2, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  0 4 −p^{2}(p − 1) ; (1, 2, 2, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  0 4  p^{2}(p − 1) ; cancel

90

(1, 2, 2, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  1 1 −p(p − 1) ; (1, 2, 2, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  1 1  p(p − 1) ; cancel (1, 2, 2, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  0 3  2 2  0 ; (1, 2, 2, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  1 2  0 ; (1, 2, 2, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  2 2  p(p − 1) ; (1, 2, 2, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  1 2  0 ; h(1, 2, 2, 4, 2) = −p + p^{2}

91

(1, 2, 2, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  1 3  −p(p − 1)^{2}

(1, 2, 2, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  0 3  2 3  p(p − 1)

(1, 2, 2, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  1 3  p(p − 1)^{2}

h(1, 2, 2, 4, 3) = −p + p^{2}

(1, 2, 2, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  1  0 4  1 4 −p^{2}(p − 1)

(1, 2, 2, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  1  0 4  1 4  p^{2}(p − 1)

cancel

(1, 2, 3, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 1  0 0  −p

h(1, 2, 3, 0, 0) = −p

(1, 2, 3, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 1  0 1  −p

h(1, 2, 3, 0, 1) = −p

\begin{matrix}(1, 2, 3, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 2  0 0 & 0 \\ (1, 2, 3, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 2  0 0 & 0 \\ (1, 2, 3, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(1, 2, 3, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 2  0 1 & 0 \\ (1, 2, 3, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 2  0 1 & 0 \\ (1, 2, 3, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(1, 2, 3, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 2  0 2 & 0 \\ (1, 2, 3, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 2  0 2 & 0 \\ (1, 2, 3, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 2  0 2 & 0 \end{matrix}

(1, 2, 3, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  0 0  0

(1, 2, 3, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 3  0 0  −p(p − 1)

h(1, 2, 3, 2, 0) = p − p^{2}

(1, 2, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  1 2  1 1  p(p − 1)^{2}

(1, 2, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 2  1 1  0

(1, 2, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 3  0 1  0

(1, 2, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  1 2  1 1  0

(1, 2, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 2  1 1  0

(1, 2, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  0 1  0

(1, 2, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 2  1 1  −p(p − 1)

(1, 2, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 3  0 1  0

h(1, 2, 3, 2, 1) = 2p − 3p^{2} + p^{3}

(1, 2, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 2  1 2  0

(1, 2, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 3  0 2  0

(1, 2, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  1 2  1 2  0

(1, 2, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 2  1 2  0

(1, 2, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  0 2  0

(1, 2, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 2  1 2  −p(p − 1)

(1, 2, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 3  0 2  −p(p − 1)^{2}

h(1, 2, 3, 2, 2) = p − p^{2}

(1, 2, 3, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 3  0 3  0 ; (1, 2, 3, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  0 3  0 ; (1, 2, 3, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 3  0 3  −p^{2}(p − 1) ; h(1, 2, 3, 2, 3) = p^{2} − p^{3} \begin{matrix}(1, 2, 3, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  0 0 & 0 \\ (1, 2, 3, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  0 0 & 0 \\ (1, 2, 3, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  0 0 & 0 \end{matrix}

97

(1, 2, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 3  1 1  0

(1, 2, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  0 1  0

(1, 2, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  1 3  1 1  0

(1, 2, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  1 1  0

(1, 2, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  0 1  0

(1, 2, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 3  1 1  0

(1, 2, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  0 1  0

h(1, 2, 3, 3, 1) = p − 2p^{2} + p^{3}

\begin{matrix}(1, 2, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  1 3  1 2 & 0 \\ (1, 2, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 3  1 2 & 0 \\ (1, 2, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  0 2 & 0 \\ (1, 2, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  1 3  1 2 & 0 \\ (1, 2, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  1 2 & 0 \\ (1, 2, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  0 2 & 0 \\ (1, 2, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 3  1 2 & 0 \\ (1, 2, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  0 2 & 0 \end{matrix}

99

(1, 2, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 3  2  1 3  1 3  −p(p − 1)^{2}

(1, 2, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 3  1 3  0

(1, 2, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  0 3  0

(1, 2, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  1 3  1 3  0

(1, 2, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  1 3  0

(1, 2, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  0 3  0

(1, 2, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 3  1 3  0

(1, 2, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  0 3  0

h(1, 2, 3, 3, 3) = −p + 2p^{2} − p^{3}

\begin{matrix}(1, 2, 3, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  0 4 & 0 \\ (1, 2, 3, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  0 4 & 0 \\ (1, 2, 3, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  0 4 & 0 \end{matrix}

(1, 2, 3, 4, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  0 0  p^{2}

h(1, 2, 3, 4, 0) = p^{2}

(1, 2, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  1 1  0

(1, 2, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  1 1  0

(1, 2, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  1 1  −p^{2}(p − 1)

(1, 2, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  0 1  0

h(1, 2, 3, 4, 1) = p^{2} − p^{3}

(1, 2, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 3  2 2  0

(1, 2, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  1 2  0

(1, 2, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  1 3  2 2  0

(1, 2, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  2 2  0

(1, 2, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  1 2  0

(1, 2, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  1 2  0

(1, 2, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  0 2  p^{2}(p − 1)

h(1, 2, 3, 4, 2) = −p + p^{2}

(1, 2, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 3  2 3  0

(1, 2, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  1 3  0

(1, 2, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 3  2  1 3  2 3  0

(1, 2, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 3  2 3  0

(1, 2, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  1 3  0

(1, 2, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  1 3  −p^{2}(p − 1)^{2}

(1, 2, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  0 3  0

h(1, 2, 3, 4, 3) = −p + p^{2} + p^{3} − p^{4}

(1, 2, 3, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  1 4  0

(1, 2, 3, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 4  1 4 −p^{3}(p − 1)

(1, 2, 3, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  0 4  p^{3}(p − 1)

cancel

(1, 2, 3, 4, 5) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  0 5  p^{4}

h(1, 2, 3, 4, 5) = p^{4}

(1, 2, 3, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  1 1  −p^{3}

h(1, 2, 3, 5, 1) = −p^{3}

\begin{matrix}(1, 2, 3, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  2 2 & 0 \\ (1, 2, 3, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  2 2 & 0 \\ (1, 2, 3, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  1 2 & 0 \end{matrix}

(1, 2, 3, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  2 3  0

(1, 2, 3, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  2 3  0

(1, 2, 3, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  1 3  −p^{3}(p − 1)

h(1, 2, 3, 5, 3) = p^{3} − p^{4}

\begin{matrix}(1, 2, 3, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  0 4  2 4 & 0 \\ (1, 2, 3, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  0 4  2 4 & 0 \\ (1, 2, 3, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  1  0 5  1 4 & 0 \end{matrix}

h(1, 2, 3, 5, 5) = p^{4}

(1, 2, 4, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 2  0 0  p

h(1, 2, 4, 1, 0) = p

(1, 2, 4, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 2  0 1 0

(1, 2, 4, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 2  0 2  −p

h(1, 2, 4, 1, 2) = −p

(1, 2, 4, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  0 0  −p(p − 1)

(1, 2, 4, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  0 0  0

h(1, 2, 4, 2, 0) = p − p^{2}

(1, 2, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  0 1  0

(1, 2, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 2  1 1  p(p − 1)

(1, 2, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 2  1 1  0

(1, 2, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  0 1  0

h(1, 2, 4, 2, 1) = −p^{2} + p^{3}

(1, 2, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 2  1 2  p(p − 1)^{2} ; (1, 2, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  0 2  −p(p − 1)^{2} ; (1, 2, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 2  1 2  p(p − 1) ; (1, 2, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 2  1 2  0 ; (1, 2, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  0 2  0 ; h(1, 2, 4, 2, 2) = −p + p^{2} (1, 2, 4, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  0 3  −p^{2}(p − 1) ; (1, 2, 4, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  0 3  0 ; h(1, 2, 4, 2, 3) = p^{2} − p^{3}

108

(1, 2, 4, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  0 0 −p(p − 1) ; (1, 2, 4, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  0 0  p(p − 1) ; cancel \begin{matrix}(1, 2, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 3  1 1 & 0 \\ (1, 2, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  1 1 & 0 \\ (1, 2, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  0 1 & 0 \\ (1, 2, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 3  1 1 & 0 \\ (1, 2, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  1 1 & 0 \\ (1, 2, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  0 1 & 0 \end{matrix}

109

(1, 2, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 3  1 2  0
(1, 2, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  1 2  0
(1, 2, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  0 2 −p(p − 1)^{2}
(1, 2, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 3  1 2  0
(1, 2, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  1 2  0
(1, 2, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  0 2  p(p − 1)^{2}

cancel

\begin{matrix}(1, 2, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 3  1 3 & 0 \\ (1, 2, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  1 3 & 0 \\ (1, 2, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  0 3 & 0 \\ (1, 2, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 3  1 3 & 0 \\ (1, 2, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  1 3 & 0 \\ (1, 2, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  0 3 & 0 \end{matrix} (1, 2, 4, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  0 4  p^{2}(p − 1) ; (1, 2, 4, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  0 4 −p^{2}(p − 1) ; cancel

111

(1, 2, 4, 4, 0) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  0 0  p^{2} ; h(1, 2, 4, 4, 0) = p^{2} (1, 2, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 4  1 1  −p(p − 1)^{2} ; (1, 2, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  1 1  0 ; (1, 2, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 4  1 1  −p(p − 1) ; (1, 2, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  1 1  0 ; (1, 2, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  0 1  0 ; h(1, 2, 4, 4, 1) = p^{2} − p^{3}

112

(1, 2, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 4  1 2  0

(1, 2, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  2 2  −p^{2}(p − 1)^{2}

(1, 2, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  1 2  0

(1, 2, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 3  2 2  p(p − 1)^{2}

(1, 2, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 4  1 2  0

(1, 2, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  2 2  0

(1, 2, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  1 2  0

(1, 2, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  0 2  p^{2}(p − 1)

h(1, 2, 4, 4, 2) = −p^{2} + p^{3}

(1, 2, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 4  1 3  −p(p − 1)^{3}

(1, 2, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 3  2 3  −p^{2}(p − 1)^{2}

(1, 2, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  1 3  0

(1, 2, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 3  2 3  p(p − 1)^{2}

(1, 2, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 4  1 3  −p(p − 1)^{2}

(1, 2, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 3  2 3  0

(1, 2, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  1 3  0

(1, 2, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  0 3  0

h(1, 2, 4, 4, 3) = −p^{2} + 2p^{3} − p^{4}

(1, 2, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 4  1 4 −p^{2}(p − 1)^{2}

(1, 2, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  1 4  0

(1, 2, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 4  1 4  −p^{2}(p − 1)

(1, 2, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  1 4  0

(1, 2, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  0 4  p^{3}(p − 1)

cancel

(1, 2, 4, 4, 5) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  0 5  p^{4}

h(1, 2, 4, 4, 5) = p^{4}

(1, 2, 4, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  1 1 0

(1, 2, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 4  2 2  p^{2}(p − 1)^{2}
(1, 2, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  2 2 −p^{2}(p − 1)^{2}
(1, 2, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 4  2 2  p^{2}(p − 1)
(1, 2, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  2 2  −p^{2}(p − 1)
(1, 2, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  1 2  0

cancel

\begin{matrix}(1, 2, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  2  1 4  2 3 & 0 \\ (1, 2, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  2 3 & 0 \\ (1, 2, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 4  2 3 & 0 \\ (1, 2, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  2 3 & 0 \\ (1, 2, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  1 3 & 0 \end{matrix}

117

(1, 2, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  2 4  p^{2}(p − 1)^{2}

(1, 2, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 4  2  1 4  2 4  −p^{2}(p − 1)

(1, 2, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 4  2 4  p^{2}(p − 1)

(1, 2, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  1 4  0

cancel

(1, 2, 4, 5, 5) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  1 5 0

(1, 2, 4, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  2 2  −p^{3}

h(1, 2, 4, 6, 2) = −p^{3}

(1, 2, 4, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  2 3  0

h(1, 2, 4, 6, 3) = −p^{3} + p^{4}

(1, 2, 4, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  0 4  3 4  p^{3}(p − 1)

(1, 2, 4, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  2 4 −p^{3}(p − 1)

cancel

(1, 2, 4, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  0 5  2 5  −p^{4}

h(1, 2, 4, 6, 5) = −p^{4}

(1, 2, 5, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 2  1 1  p^{2}

h(1, 2, 5, 2, 1) = p^{2}

(1, 2, 5, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 2  1 2  p^{2}

h(1, 2, 5, 2, 2) = p^{2}

(1, 2, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 3  1 1  −p^{2}(p − 1)
(1, 2, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 3  1 1  0

h(1, 2, 5, 3, 1) = p^{2} − p^{3}

\begin{matrix}(1, 2, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 3  1 2 & 0 \\ (1, 2, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 3  1 2 & 0 \end{matrix}
(1, 2, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 3  1 3  p^{2}(p − 1)
(1, 2, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 3  1 3  0

h(1, 2, 5, 3, 3) = −p^{2} + p^{3}

(1, 2, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 4  1 1 −p^{2}(p − 1)
(1, 2, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 4  1 1  p^{2}(p − 1)

cancel

(1, 2, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 3  2 2  0 ; (1, 2, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 4  1 2  0 ; (1, 2, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 3  2 2  p^{2}(p − 1) ; (1, 2, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 4  1 2  0 ; h(1, 2, 5, 4, 2) = −p^{2} + p^{3} (1, 2, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 3  2 3  0 ; (1, 2, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 4  1 3  −p^{2}(p − 1)^{2} ; (1, 2, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 3  2 3  p^{2}(p − 1) ; (1, 2, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 4  1 3  p^{2}(p − 1)^{2} ; h(1, 2, 5, 4, 3) = −p^{2} + p^{3}

121

(1, 2, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 4  1 4 −p^{3}(p − 1)

(1, 2, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 4  1 4  p^{3}(p − 1)

cancel

(1, 2, 5, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  1 1  p^{3}

h(1, 2, 5, 5, 1) = p^{3}

\begin{matrix}(1, 2, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 4  2 2 & 0 \\ (1, 2, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 4  2 2 & 0 \\ (1, 2, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  1 2 & 0 \end{matrix}

(1, 2, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 4  2 3  0

(1, 2, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  1 3  p^{3}(p − 1)

h(1, 2, 5, 5, 3) = −p^{3} + p^{4}

\begin{matrix}(1, 2, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 4  2 4 & 0 \\ (1, 2, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 4  2 4 & 0 \\ (1, 2, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  1 4 & 0 \end{matrix}

(1, 2, 5, 5, 5) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  1 5  −p^{4}

h(1, 2, 5, 5, 5) = −p^{4}

(1, 2, 5, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  2 2  −p^{3}

h(1, 2, 5, 6, 2) = −p^{3}

(1, 2, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  2 3  0

h(1, 2, 5, 6, 3) = −p^{3} + p^{4}

(1, 2, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  1  0 4  3  1 4  3 4  p^{3}(p − 1)

(1, 2, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  2 4 −p^{3}(p − 1)

cancel

(1, 2, 5, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  2  1  0 5  2  1 5  2 5  −p^{4}

h(1, 2, 5, 6, 5) = −p^{4}

(1, 3, 1, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 1  0 0  p

h(1, 3, 1, 0, 0) = p

(1, 3, 1, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 1  0 1  p

h(1, 3, 1, 0, 1) = p

(1, 3, 1, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 2  0 0 0

(1, 3, 1, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 2  0 1 0

(1, 3, 1, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 2  0 2 0

(1, 3, 1, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 3  0 0  −p

h(1, 3, 1, 2, 0) = −p

(1, 3, 1, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 2  1 1  p(p − 1)

(1, 3, 1, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 3  0 1  0

h(1, 3, 1, 2, 1) = −p + p^{2}

(1, 3, 1, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 2  1 2  p(p − 1)

(1, 3, 1, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 3  0 2 −p(p − 1)

cancel

(1, 3, 1, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 3  0 3  −p^{2}

h(1, 3, 1, 2, 3) = −p^{2}

h(1, 3, 1, 3, 1) = p^{2}

(1, 3, 1, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 3  1 2 0

(1, 3, 1, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  1  0 3  1 3  −p^{2}

h(1, 3, 1, 3, 3) = −p^{2}

(1, 3, 2, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 1  0 0 0

(1, 3, 2, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 1  0 1 0

\begin{matrix}(1, 3, 2, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 2  0 0 & 0 \\ (1, 3, 2, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 2  0 0 & 0 \\ (1, 3, 2, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(1, 3, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 2  0 1 & 0 \\ (1, 3, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 2  0 1 & 0 \\ (1, 3, 2, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(1, 3, 2, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 2  0 2 & 0 \\ (1, 3, 2, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 2  0 2 & 0 \\ (1, 3, 2, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 2  0 2 & 0 \end{matrix}

\begin{matrix}(1, 3, 2, 2, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  0 0 & 0 \\ (1, 3, 2, 2, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  0 0 & 0 \\ (1, 3, 2, 2, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 3  0 0 & 0 \end{matrix}

\begin{matrix}(1, 3, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 2  1 1 & 0 \\ (1, 3, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  0 1 & 0 \\ (1, 3, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 2  1 1 & 0 \\ (1, 3, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  0 1 & 0 \\ (1, 3, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 2  1 1 & 0 \\ (1, 3, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 3  0 1 & 0 \end{matrix}

128

\begin{matrix}(1, 3, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 2  1 2 & 0 \\ (1, 3, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  0 2 & 0 \\ (1, 3, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 2  1 2 & 0 \\ (1, 3, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  0 2 & 0 \\ (1, 3, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 2  1 2 & 0 \\ (1, 3, 2, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 3  0 2 & 0 \end{matrix} \begin{matrix}(1, 3, 2, 2, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  0 3 & 0 \\ (1, 3, 2, 2, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  0 3 & 0 \\ (1, 3, 2, 2, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 3  0 3 & 0 \end{matrix}

129

(1, 3, 2, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  0 0 0

\begin{matrix}(1, 3, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  1 1 & 0 \\ (1, 3, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  1 1 & 0 \\ (1, 3, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 3  1 1 & 0 \\ (1, 3, 2, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  0 1 & 0 \end{matrix}

\begin{matrix}(1, 3, 2, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  1 2 & 0 \\ (1, 3, 2, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  1 2 & 0 \\ (1, 3, 2, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 3  1 2 & 0 \\ (1, 3, 2, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  0 2 & 0 \end{matrix}

\begin{matrix}(1, 3, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  1 3 & 0 \\ (1, 3, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  1 3 & 0 \\ (1, 3, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 3  1 3 & 0 \\ (1, 3, 2, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  0 3 & 0 \end{matrix}

(1, 3, 2, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  0 4 0

(1, 3, 2, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  1 1 0

\begin{matrix}(1, 3, 2, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  2 2 & 0 \\ (1, 3, 2, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  2 2 & 0 \\ (1, 3, 2, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(1, 3, 2, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  0 3  2 3 & 0 \\ (1, 3, 2, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  0 3  2 3 & 0 \\ (1, 3, 2, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  1 3 & 0 \end{matrix}

(1, 3, 2, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  1  0 4  1 4 0

(1, 3, 3, 0, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 1  0 0  −p

h(1, 3, 3, 0, 0) = −p

(1, 3, 3, 0, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 1  0 1  −p

h(1, 3, 3, 0, 1) = −p

\begin{matrix}(1, 3, 3, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 2  0 0 & 0 \\ (1, 3, 3, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 2  0 0 & 0 \\ (1, 3, 3, 1, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(1, 3, 3, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 2  0 1 & 0 \\ (1, 3, 3, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 2  0 1 & 0 \\ (1, 3, 3, 1, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(1, 3, 3, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 2  0 2 & 0 \\ (1, 3, 3, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 2  0 2 & 0 \\ (1, 3, 3, 1, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 2  0 2 & 0 \end{matrix}

(1, 3, 3, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  0 0  0

(1, 3, 3, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 3  0 0  −p(p − 1)

h(1, 3, 3, 2, 0) = p − p^{2}

(1, 3, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 2  1 1  0

(1, 3, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 3  0 1  0

(1, 3, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  1 2  1 1  p^{2}(p − 1)

(1, 3, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 2  1 1  0

(1, 3, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  0 1  0

(1, 3, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 2  1 1  −p(p − 1)

(1, 3, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 3  0 1  0

h(1, 3, 3, 2, 1) = p − 2p^{2} + p^{3}

(1, 3, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  1 2  1 2  0
(1, 3, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 2  1 2  0
(1, 3, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 3  0 2  0
(1, 3, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  1 2  1 2  p^{2}(p − 1)
(1, 3, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 2  1 2  0
(1, 3, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  0 2  0
(1, 3, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 2  1 2  −p(p − 1)
(1, 3, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 3  0 2 −p(p − 1)^{2}

cancel

(1, 3, 3, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 3  0 3  0 ; (1, 3, 3, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  0 3  0 ; (1, 3, 3, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 3  0 3  −p^{2}(p − 1) ; h(1, 3, 3, 2, 3) = p^{2} − p^{3} \begin{matrix}(1, 3, 3, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  0 0 & 0 \\ (1, 3, 3, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  0 0 & 0 \\ (1, 3, 3, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  0 0 & 0 \end{matrix}

137

(1, 3, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 3  1 1  0

(1, 3, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  0 1  0

(1, 3, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  1 3  1 1  p^{2}(p − 1)

(1, 3, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  1 1  0

(1, 3, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  0 1  0

(1, 3, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 3  1 1  0

(1, 3, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  0 1  0

h(1, 3, 3, 3, 1) = −p^{2} + p^{3}

\begin{matrix}(1, 3, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  1 3  1 2 & 0 \\ (1, 3, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 3  1 2 & 0 \\ (1, 3, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  0 2 & 0 \\ (1, 3, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  1 3  1 2 & 0 \\ (1, 3, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  1 2 & 0 \\ (1, 3, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  0 2 & 0 \\ (1, 3, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 3  1 2 & 0 \\ (1, 3, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  0 2 & 0 \end{matrix}

139

(1, 3, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 3  1 3  0

(1, 3, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  0 3  0

(1, 3, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  1 3  1 3  −p^{2}(p − 1)

(1, 3, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  1 3  0

(1, 3, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  0 3  0

(1, 3, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 3  1 3  0

(1, 3, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  0 3  0

h(1, 3, 3, 3, 3) = p^{2} − p^{3}

\begin{matrix}(1, 3, 3, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  0 4 & 0 \\ (1, 3, 3, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  0 4 & 0 \\ (1, 3, 3, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  0 4 & 0 \end{matrix}

(1, 3, 3, 4, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  0 0  p^{2}

h(1, 3, 3, 4, 0) = p^{2}

(1, 3, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  1 1  0

(1, 3, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  1 1  0

(1, 3, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  1 1  −p^{2}(p − 1)

(1, 3, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  0 1  0

h(1, 3, 3, 4, 1) = p^{2} − p^{3}

(1, 3, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 3  2  1 3  2 2  0
(1, 3, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 3  2 2  0
(1, 3, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  1 2  0
(1, 3, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  1 3  2 2 −p^{2}(p − 1)
(1, 3, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  2 2  0
(1, 3, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  1 2  0
(1, 3, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  1 2  0
(1, 3, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  0 2  p^{2}(p − 1)

cancel

(1, 3, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 3  2 3  0

(1, 3, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  1 3  0

(1, 3, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 3  2  1 3  2 3  −p^{2}(p − 1)

(1, 3, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 3  2 3  0

(1, 3, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  1 3  0

(1, 3, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  1 3  −p^{2}(p − 1)^{2}

(1, 3, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  0 3  0

h(1, 3, 3, 4, 3) = p^{3} − p^{4}

(1, 3, 3, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  1 4  0

(1, 3, 3, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 4  1 4 −p^{3}(p − 1)

(1, 3, 3, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  0 4  p^{3}(p − 1)

cancel

(1, 3, 3, 4, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  0 5  p^{4}

h(1, 3, 3, 4, 5) = p^{4}

(1, 3, 3, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  1 1  −p^{3}

h(1, 3, 3, 5, 1) = −p^{3}

\begin{matrix}(1, 3, 3, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  2 2 & 0 \\ (1, 3, 3, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  2 2 & 0 \\ (1, 3, 3, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  1 2 & 0 \end{matrix}

(1, 3, 3, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  2 3  0

(1, 3, 3, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  2 3  0

(1, 3, 3, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  1 3  −p^{3}(p − 1)

h(1, 3, 3, 5, 3) = p^{3} − p^{4}

\begin{matrix}(1, 3, 3, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  0 4  2 4 & 0 \\ (1, 3, 3, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  0 4  2 4 & 0 \\ (1, 3, 3, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  1  0 5  1 4 & 0 \end{matrix}

h(1, 3, 3, 5, 5) = p^{4}

(1, 3, 4, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 2  0 0 0

(1, 3, 4, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 2  0 1 0

(1, 3, 4, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 2  0 2 0

\begin{matrix}(1, 3, 4, 2, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  0 0 & 0 \\ (1, 3, 4, 2, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  0 0 & 0 \\ (1, 3, 4, 2, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  0 0 & 0 \end{matrix}

\begin{matrix}(1, 3, 4, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 2  1 1 & 0 \\ (1, 3, 4, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  0 1 & 0 \\ (1, 3, 4, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 2  1 1 & 0 \\ (1, 3, 4, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  0 1 & 0 \\ (1, 3, 4, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 2  1 1 & 0 \\ (1, 3, 4, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  0 1 & 0 \end{matrix}

147

\begin{matrix}(1, 3, 4, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 2  1 2 & 0 \\ (1, 3, 4, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  0 2 & 0 \\ (1, 3, 4, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 2  1 2 & 0 \\ (1, 3, 4, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  0 2 & 0 \\ (1, 3, 4, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 2  1 2 & 0 \\ (1, 3, 4, 2, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  0 2 & 0 \end{matrix} \begin{matrix}(1, 3, 4, 2, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  0 3 & 0 \\ (1, 3, 4, 2, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  0 3 & 0 \\ (1, 3, 4, 2, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  0 3 & 0 \end{matrix}

148

\begin{matrix}(1, 3, 4, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  0 0 & 0 \\ (1, 3, 4, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  0 0 & 0 \\ (1, 3, 4, 3, 0) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  0 0 & 0 \end{matrix}

149

\begin{matrix}(1, 3, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 3  1 1 & 0 \\ (1, 3, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  1 1 & 0 \\ (1, 3, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  0 1 & 0 \\ (1, 3, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 3  1 1 & 0 \\ (1, 3, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  1 1 & 0 \\ (1, 3, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  0 1 & 0 \\ (1, 3, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  1 1 & 0 \\ (1, 3, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  0 1 & 0 \end{matrix}

150

\begin{matrix}(1, 3, 4, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 3  1 2 & 0 \\ (1, 3, 4, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  1 2 & 0 \\ (1, 3, 4, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  0 2 & 0 \\ (1, 3, 4, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 3  1 2 & 0 \\ (1, 3, 4, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  1 2 & 0 \\ (1, 3, 4, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  0 2 & 0 \\ (1, 3, 4, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  1 2 & 0 \\ (1, 3, 4, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  0 2 & 0 \end{matrix}

151

\begin{matrix}(1, 3, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 3  1 3 & 0 \\ (1, 3, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  1 3 & 0 \\ (1, 3, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  0 3 & 0 \\ (1, 3, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 3  1 3 & 0 \\ (1, 3, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  1 3 & 0 \\ (1, 3, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  0 3 & 0 \\ (1, 3, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  1 3 & 0 \\ (1, 3, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  0 3 & 0 \end{matrix}

152

\begin{matrix}(1, 3, 4, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  0 4 & 0 \\ (1, 3, 4, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  0 4 & 0 \\ (1, 3, 4, 3, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  0 4 & 0 \end{matrix} (1, 3, 4, 4, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  0 0 0

153

\begin{matrix}(1, 3, 4, 4, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 4  1 1 & 0 \\ (1, 3, 4, 4, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  1 1 & 0 \\ (1, 3, 4, 4, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 4  1 1 & 0 \\ (1, 3, 4, 4, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  1 1 & 0 \\ (1, 3, 4, 4, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  1 1 & 0 \\ (1, 3, 4, 4, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  0 1 & 0 \end{matrix}

154

\begin{matrix}(1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 3  2 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 4  1 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  2 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  1 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 3  2 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 4  1 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  2 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  1 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  2 2 & 0 \end{matrix}

155

\begin{matrix}(1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  1 2 & 0 \\ (1, 3, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  0 2 & 0 \end{matrix}

156

\begin{matrix}(1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 3  2 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 4  1 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 3  2 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  1 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 3  2 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 4  1 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 3  2 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  1 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 3  2 3 & 0 \end{matrix}

157

\begin{matrix}(1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  1 3 & 0 \\ (1, 3, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  0 3 & 0 \end{matrix}

\begin{matrix}(1, 3, 4, 4, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 4  1 4 & 0 \\ (1, 3, 4, 4, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  1 4 & 0 \\ (1, 3, 4, 4, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 4  1 4 & 0 \\ (1, 3, 4, 4, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  1 4 & 0 \\ (1, 3, 4, 4, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  1 4 & 0 \\ (1, 3, 4, 4, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  0 4 & 0 \end{matrix}

(1, 3, 4, 4, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  0 5 0

(1, 3, 4, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  1 1 0 \begin{matrix}(1, 3, 4, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 4  2 2 & 0 \\ (1, 3, 4, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  2 2 & 0 \\ (1, 3, 4, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 4  2 2 & 0 \\ (1, 3, 4, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  2 2 & 0 \\ (1, 3, 4, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  2 2 & 0 \\ (1, 3, 4, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  1 2 & 0 \end{matrix}

159

\begin{matrix}(1, 3, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 4  2 3 & 0 \\ (1, 3, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  2 3 & 0 \\ (1, 3, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 4  2 3 & 0 \\ (1, 3, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  2 3 & 0 \\ (1, 3, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  2 3 & 0 \\ (1, 3, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  1 3 & 0 \end{matrix}

160

\begin{matrix}(1, 3, 4, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  2  1 4  2 4 & 0 \\ (1, 3, 4, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  2 4 & 0 \\ (1, 3, 4, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  2  1 4  2 4 & 0 \\ (1, 3, 4, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  2 4 & 0 \\ (1, 3, 4, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 4  2 4 & 0 \\ (1, 3, 4, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  1 4 & 0 \end{matrix}

(1, 3, 4, 5, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  1 5 0

(1, 3, 4, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  2 2 0

\begin{matrix}(1, 3, 4, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  3 3 & 0 \\ (1, 3, 4, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  3 3 & 0 \\ (1, 3, 4, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  2 3 & 0 \end{matrix}

\begin{matrix}(1, 3, 4, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  0 4  3 4 & 0 \\ (1, 3, 4, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  0 4  3 4 & 0 \\ (1, 3, 4, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  2 4 & 0 \end{matrix}

(1, 3, 4, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  0 5  2 5 0

(1, 3, 5, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  0 0  p^{2}

h(1, 3, 5, 2, 0) = p^{2}

(1, 3, 5, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  0 1  0

h(1, 3, 5, 2, 1) = p^{2} − p^{3}

(1, 3, 5, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 2  1 2 −p^{2}(p − 1)

(1, 3, 5, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  0 2  p^{2}(p − 1)

cancel

(1, 3, 5, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  0 3  p^{3}

h(1, 3, 5, 2, 3) = p^{3}

(1, 3, 5, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  0 0 0

(1, 3, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 3  1 1  p^{3}(p − 1)

(1, 3, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 3  1 1  0

(1, 3, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  1 1  0

(1, 3, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  0 1  0

h(1, 3, 5, 3, 1) = −p^{3} + p^{4}

\begin{matrix}(1, 3, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  1 3  1 2 & 0 \\ (1, 3, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 3  1 2 & 0 \\ (1, 3, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 3  1 2 & 0 \\ (1, 3, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  1 2 & 0 \\ (1, 3, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  0 2 & 0 \end{matrix}

165

(1, 3, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 3  1 3  −p^{3}(p − 1)

(1, 3, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 3  1 3  0

(1, 3, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  1 3  0

(1, 3, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  0 3  0

h(1, 3, 5, 3, 3) = p^{3} − p^{4}

(1, 3, 5, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  0 4 0

(1, 3, 5, 4, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  0 0  −p^{2}

h(1, 3, 5, 4, 0) = −p^{2}

(1, 3, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  1 1  p^{3}(p − 1)

(1, 3, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 4  1 1  −p^{2}(p − 1)^{2}

(1, 3, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  1 1  0

(1, 3, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  0 1  0

h(1, 3, 5, 4, 1) = −p^{2} + p^{3}

(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  1 3  2 2  0
(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  1 4  1 2  0
(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 3  2 2  0
(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  1 2  0
(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 3  2 2 −p^{2}(p − 1)^{2}
(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 4  1 2  0
(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  2 2  p^{3}(p − 1)
(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  1 2  0
(1, 3, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  0 2  −p^{2}(p − 1)

cancel

(1, 3, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  1 4  1 3  0

(1, 3, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 3  2 3  0

(1, 3, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  1 3  p^{3}(p − 1)^{2}

(1, 3, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 3  2 3  −p^{2}(p − 1)^{2}

(1, 3, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 4  1 3  −p^{2}(p − 1)^{3}

(1, 3, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 3  2 3  p^{3}(p − 1)

(1, 3, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  1 3  0

(1, 3, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  0 3  0

h(1, 3, 5, 4, 3) = −p^{3} + p^{4}

(1, 3, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  1 4  p^{4}(p − 1)

(1, 3, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 4  1 4 −p^{3}(p − 1)^{2}

(1, 3, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  1 4  0

(1, 3, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  0 4  −p^{3}(p − 1)

cancel

(1, 3, 5, 4, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  0 5  −p^{4}

h(1, 3, 5, 4, 5) = −p^{4}

(1, 3, 5, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  1 1  −p^{3}(p − 1)

(1, 3, 5, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  1 1  0

h(1, 3, 5, 5, 1) = p^{3} − p^{4}

\begin{matrix}(1, 3, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  1 4  2 2 & 0 \\ (1, 3, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  2 2 & 0 \\ (1, 3, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 4  2 2 & 0 \\ (1, 3, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  1 2 & 0 \\ (1, 3, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  2 2 & 0 \\ (1, 3, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  1 2 & 0 \end{matrix}

171

(1, 3, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  2 3  0

(1, 3, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 4  2 3  0

(1, 3, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  1 3  −p^{3}(p − 1)^{2}

(1, 3, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  2 3  0

(1, 3, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  1 3  0

h(1, 3, 5, 5, 3) = −p^{3} + 2p^{4} − p^{5}

\begin{matrix}(1, 3, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  1 4  2 4 & 0 \\ (1, 3, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  2 4 & 0 \\ (1, 3, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 4  2 4 & 0 \\ (1, 3, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  1 4 & 0 \\ (1, 3, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  2 4 & 0 \\ (1, 3, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  1 4 & 0 \end{matrix} (1, 3, 5, 5, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  1 5  p^{4}(p − 1) ; (1, 3, 5, 5, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  1 5  0 ; h(1, 3, 5, 5, 5) = −p^{4} + p^{5}

173

(1, 3, 5, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  2 2  p^{3}(p − 1)
(1, 3, 5, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  2 2 −p^{3}(p − 1)

cancel

(1, 3, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  1 4  3 3  0
(1, 3, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  3 3 −p^{4}(p − 1)
(1, 3, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  2 3  0
(1, 3, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  3 3  p^{4}(p − 1)
(1, 3, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  2 3  0

cancel

(1, 3, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 4  3  1 4  3 4  −p^{4}(p − 1)

(1, 3, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  2 4  p^{3}(p − 1)^{2}

(1, 3, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 4  3 4  p^{4}(p − 1)

(1, 3, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  2 4 −p^{3}(p − 1)^{2}

cancel

(1, 3, 5, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  2  1 5  2 5  p^{4}(p − 1)

(1, 3, 5, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  2 5 −p^{4}(p − 1)

cancel

(1, 3, 5, 7, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  3 3  p^{5}

h(1, 3, 5, 7, 3) = p^{5}

(1, 3, 5, 7, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  3 4 0

(1, 3, 5, 7, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  0 5  3 5  −p^{5}

h(1, 3, 5, 7, 5) = −p^{5}

(1, 3, 6, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 3  1 1  p^{4}

h(1, 3, 6, 3, 1) = p^{4}

(1, 3, 6, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 3  1 2 0

(1, 3, 6, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 3  1 3  −p^{4}

h(1, 3, 6, 3, 3) = −p^{4}

(1, 3, 6, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  1 1 0

\begin{matrix}(1, 3, 6, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  2 3  2 2 & 0 \\ (1, 3, 6, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 3  2 2 & 0 \\ (1, 3, 6, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(1, 3, 6, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  2 3  2 3 & 0 \\ (1, 3, 6, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 3  2 3 & 0 \\ (1, 3, 6, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  1 3 & 0 \end{matrix}

(1, 3, 6, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  1 4 0

(1, 3, 6, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  1 1  −p^{4}

h(1, 3, 6, 5, 1) = −p^{4}

\begin{matrix}(1, 3, 6, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  2 4  2 2 & 0 \\ (1, 3, 6, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  2 2 & 0 \\ (1, 3, 6, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  1 2 & 0 \end{matrix}

(1, 3, 6, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  2 4  2 3  0

(1, 3, 6, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  2 3  0

(1, 3, 6, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  1 3  −p^{4}(p − 1)

h(1, 3, 6, 5, 3) = p^{4} − p^{5}

\begin{matrix}(1, 3, 6, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  2 4  2 4 & 0 \\ (1, 3, 6, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  2 4 & 0 \\ (1, 3, 6, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  1 4 & 0 \end{matrix}

h(1, 3, 6, 5, 5) = p^{5}

(1, 3, 6, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  2 2 0

\begin{matrix}(1, 3, 6, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  2 4  3 3 & 0 \\ (1, 3, 6, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  3 3 & 0 \\ (1, 3, 6, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  2 3 & 0 \end{matrix}

\begin{matrix}(1, 3, 6, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  0 4  3  2 4  3 4 & 0 \\ (1, 3, 6, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 4  3 4 & 0 \\ (1, 3, 6, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  2 4 & 0 \end{matrix}

(1, 3, 6, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  2 5 0

h(1, 3, 6, 7, 3) = p^{5}

(1, 3, 6, 7, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  3 4 0

(1, 3, 6, 7, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  1  0 5  3  1 5  3 5  −p^{5}

h(1, 3, 6, 7, 5) = −p^{5}

(1, 4, 2, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 2  0 0  p

h(1, 4, 2, 1, 0) = p

(1, 4, 2, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 2  0 1 0

(1, 4, 2, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 2  0 2  −p

h(1, 4, 2, 1, 2) = −p

(1, 4, 2, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 3  0 0  p

h(1, 4, 2, 2, 0) = p

\begin{matrix}(1, 4, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 2  1 1 & 0 \\ (1, 4, 2, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 3  0 1 & 0 \end{matrix}

(1, 4, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 2  1 2  0

(1, 4, 2, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 3  0 2  p(p − 1)

h(1, 4, 2, 2, 2) = −p + p^{2}

(1, 4, 2, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 3  0 3  p^{2}

h(1, 4, 2, 2, 3) = p^{2}

(1, 4, 2, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 3  1 1 0

(1, 4, 2, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 3  1 2 0

(1, 4, 2, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 3  1 3 0

h(1, 4, 2, 4, 2) = −p^{2}

(1, 4, 2, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  0 3  2 3  −p^{2}

h(1, 4, 2, 4, 3) = −p^{2}

(1, 4, 3, 1, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 2  0 0 0

(1, 4, 3, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 2  0 1 0

(1, 4, 3, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 2  0 2 0

(1, 4, 3, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  0 0 0

(1, 4, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 3  2  1 2  1 1  −p^{2}(p − 1) ; (1, 4, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  1 2  1 1  0 ; (1, 4, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 2  1 1  0 ; (1, 4, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  0 1  0 ; h(1, 4, 3, 2, 1) = p^{2} − p^{3} (1, 4, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 3  2  1 2  1 2  −p^{2}(p − 1) ; (1, 4, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  1 2  1 2  0 ; (1, 4, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 2  1 2  0 ; (1, 4, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  0 2  0 ; h(1, 4, 3, 2, 2) = p^{2} − p^{3}

183

(1, 4, 3, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  0 3 0

(1, 4, 3, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  0 0 0

(1, 4, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 3  2  1 3  1 1  −p^{2}(p − 1)

(1, 4, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  1 3  1 1  0

(1, 4, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  1 1  0

(1, 4, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  0 1  0

h(1, 4, 3, 3, 1) = p^{2} − p^{3}

\begin{matrix}(1, 4, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 3  2  1 3  1 2 & 0 \\ (1, 4, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  1 3  1 2 & 0 \\ (1, 4, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  1 2 & 0 \\ (1, 4, 3, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  0 2 & 0 \end{matrix}

(1, 4, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 3  2  1 3  1 3  p^{2}(p − 1)

(1, 4, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  1 3  1 3  0

(1, 4, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  1 3  0

(1, 4, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  0 3  0

h(1, 4, 3, 3, 3) = −p^{2} + p^{3}

(1, 4, 3, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  0 4 0

(1, 4, 3, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  1 1 0 (1, 4, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 3  2  1 3  2 2  p^{2}(p − 1) ; (1, 4, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  1 3  2 2  0 ; (1, 4, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  2 2  0 ; (1, 4, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  1 2  0 ; h(1, 4, 3, 4, 2) = −p^{2} + p^{3}

186

(1, 4, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 3  2  1 3  2 3  0

(1, 4, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 3  2 3  0

(1, 4, 3, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  1 3  0

h(1, 4, 3, 4, 3) = −p^{2} + p^{3}

(1, 4, 3, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  1 4 0

(1, 4, 3, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  2 2 0

(1, 4, 3, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  2 3 0

(1, 4, 3, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  0 4  2 4 0

h(1, 4, 4, 1, 0) = −p

(1, 4, 4, 1, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 2  0 1 0

(1, 4, 4, 1, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 2  0 2  p

h(1, 4, 4, 1, 2) = p

(1, 4, 4, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  0 0  p(p − 1)

(1, 4, 4, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  0 0  0

h(1, 4, 4, 2, 0) = −p + p^{2}

(1, 4, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 2  1 1  0

(1, 4, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  0 1  0

(1, 4, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 2  1 1  0

(1, 4, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  0 1  0

h(1, 4, 4, 2, 1) = p^{2} − p^{3}

(1, 4, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 2  1 2  −p^{2}(p − 1) ; (1, 4, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 2  1 2  0 ; (1, 4, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  0 2  p(p − 1)^{2} ; (1, 4, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 2  1 2  0 ; (1, 4, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  0 2  0 ; h(1, 4, 4, 2, 2) = p − p^{2} (1, 4, 4, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  0 3  p^{2}(p − 1) ; (1, 4, 4, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  0 3  0 ; h(1, 4, 4, 2, 3) = −p^{2} + p^{3}

190

(1, 4, 4, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  0 0  p(p − 1) ; (1, 4, 4, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  0 0 −p(p − 1) ; cancel \begin{matrix}(1, 4, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 3  1 1 & 0 \\ (1, 4, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 3  1 1 & 0 \\ (1, 4, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  1 1 & 0 \\ (1, 4, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  0 1 & 0 \\ (1, 4, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  1 1 & 0 \\ (1, 4, 4, 3, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  0 1 & 0 \end{matrix}

191

(1, 4, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 3  1 2  0
(1, 4, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 3  1 2  0
(1, 4, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  1 2  0
(1, 4, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  0 2  p(p − 1)^{2}
(1, 4, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  1 2  0
(1, 4, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  0 2 −p(p − 1)^{2}

cancel

\begin{matrix}(1, 4, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 3  1 3 & 0 \\ (1, 4, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 3  1 3 & 0 \\ (1, 4, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  1 3 & 0 \\ (1, 4, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  0 3 & 0 \\ (1, 4, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  1 3 & 0 \\ (1, 4, 4, 3, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  0 3 & 0 \end{matrix} (1, 4, 4, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  0 4 −p^{2}(p − 1) ; (1, 4, 4, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  0 4  p^{2}(p − 1) ; cancel

193

(1, 4, 4, 4, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  0 0  −p^{2} ; h(1, 4, 4, 4, 0) = −p^{2} (1, 4, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 4  1 1  p^{2}(p − 1) ; (1, 4, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 4  1 1  0 ; (1, 4, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  1 1  0 ; (1, 4, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  1 1  0 ; (1, 4, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  0 1  0 ; h(1, 4, 4, 4, 1) = −p^{2} + p^{3}

194

(1, 4, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 4  1 2  0

(1, 4, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 3  2 2  0

(1, 4, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 4  1 2  0

(1, 4, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  2 2  p^{2}(p − 1)^{2}

(1, 4, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  1 2  0

(1, 4, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  2 2  0

(1, 4, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  1 2  0

(1, 4, 4, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  0 2  −p^{2}(p − 1)

h(1, 4, 4, 4, 2) = p^{2} − p^{3}

(1, 4, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 4  1 3  p^{2}(p − 1)^{2}

(1, 4, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 3  2 3  0

(1, 4, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 4  1 3  0

(1, 4, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 3  2 3  p^{2}(p − 1)^{2}

(1, 4, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  1 3  0

(1, 4, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 3  2 3  0

(1, 4, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  1 3  0

(1, 4, 4, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  0 3  0

h(1, 4, 4, 4, 3) = p^{2} − 2p^{3} + p^{4}

(1, 4, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 4  1 4  0

(1, 4, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  1 4  0

(1, 4, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  1 4  0

(1, 4, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  0 4 −p^{3}(p − 1)

cancel

(1, 4, 4, 4, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  0 5  −p^{4}

h(1, 4, 4, 4, 5) = −p^{4}

(1, 4, 4, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  1 1 0

(1, 4, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 4  2 2 −p^{3}(p − 1)
(1, 4, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 4  2 2  0
(1, 4, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  2 2  p^{2}(p − 1)^{2}
(1, 4, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  2 2  p^{2}(p − 1)
(1, 4, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  1 2  0

cancel

\begin{matrix}(1, 4, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  2  1 4  2 3 & 0 \\ (1, 4, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 4  2 3 & 0 \\ (1, 4, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  2 3 & 0 \\ (1, 4, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  2 3 & 0 \\ (1, 4, 4, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  1 3 & 0 \end{matrix}

199

(1, 4, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  2  1 4  2 4  0

(1, 4, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  2 4 −p^{2}(p − 1)^{2}

(1, 4, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 4  2 4  −p^{2}(p − 1)

(1, 4, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  1 4  0

cancel

(1, 4, 4, 5, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  1 5 0

(1, 4, 4, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  2 2  p^{3}

h(1, 4, 4, 6, 2) = p^{3}

(1, 4, 4, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  2 3  0

h(1, 4, 4, 6, 3) = p^{3} − p^{4}

(1, 4, 4, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  0 4  3 4 −p^{3}(p − 1)

(1, 4, 4, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  2 4  p^{3}(p − 1)

cancel

(1, 4, 4, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  0 5  2 5  p^{4}

h(1, 4, 4, 6, 5) = p^{4}

(1, 4, 5, 2, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  0 0  p^{2}

h(1, 4, 5, 2, 0) = p^{2}

\begin{matrix}(1, 4, 5, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 2  1 1 & 0 \\ (1, 4, 5, 2, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  0 1 & 0 \end{matrix}

(1, 4, 5, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  0 2  p^{2}(p − 1)

h(1, 4, 5, 2, 2) = −p^{2} + p^{3}

(1, 4, 5, 2, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  0 3  p^{3}

h(1, 4, 5, 2, 3) = p^{3}

(1, 4, 5, 3, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  0 0 0

(1, 4, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 3  1 1  0

(1, 4, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 3  1 1  0

(1, 4, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  1 1  0

(1, 4, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  0 1  0

h(1, 4, 5, 3, 1) = −p^{2} + p^{3}

\begin{matrix}(1, 4, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  1 3  1 2 & 0 \\ (1, 4, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 3  1 2 & 0 \\ (1, 4, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 3  1 2 & 0 \\ (1, 4, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  1 2 & 0 \\ (1, 4, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  0 2 & 0 \end{matrix}

204

(1, 4, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 3  1 3  0

(1, 4, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 3  1 3  0

(1, 4, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  1 3  0

(1, 4, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  0 3  0

h(1, 4, 5, 3, 3) = p^{2} − p^{3}

(1, 4, 5, 3, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  0 4 0

(1, 4, 5, 4, 0) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  0 0  −p^{2}

h(1, 4, 5, 4, 0) = −p^{2}

(1, 4, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  1 1  0

(1, 4, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 4  1 1  0

(1, 4, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  1 1  0

(1, 4, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  0 1  0

h(1, 4, 5, 4, 1) = −p^{2} + p^{3}

(1, 4, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  1 4  1 2  0

(1, 4, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 3  2 2  0

(1, 4, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  1 2  0

(1, 4, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 3  2 2  0

(1, 4, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 4  1 2  0

(1, 4, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  2 2  p^{3}(p − 1)

(1, 4, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  1 2  0

(1, 4, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  0 2  −p^{2}(p − 1)

h(1, 4, 5, 4, 2) = p^{2} − 2p^{3} + p^{4}

(1, 4, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  1 4  1 3  p^{2}(p − 1)^{2}

(1, 4, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 3  2 3  0

(1, 4, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  1 3  0

(1, 4, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 3  2 3  0

(1, 4, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 4  1 3  0

(1, 4, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 3  2 3  p^{3}(p − 1)

(1, 4, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  1 3  0

(1, 4, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  0 3  0

h(1, 4, 5, 4, 3) = p^{2} − 3p^{3} + 2p^{4}

(1, 4, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  1 4  0

(1, 4, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 4  1 4  0

(1, 4, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  1 4  0

(1, 4, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  0 4 −p^{3}(p − 1)

cancel

(1, 4, 5, 4, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  0 5  −p^{4}

h(1, 4, 5, 4, 5) = −p^{4}

\begin{matrix}(1, 4, 5, 5, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  1 1 & 0 \\ (1, 4, 5, 5, 1) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  1 1 & 0 \end{matrix}

\begin{matrix}(1, 4, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  1 4  2 2 & 0 \\ (1, 4, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  2 2 & 0 \\ (1, 4, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 4  2 2 & 0 \\ (1, 4, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  1 2 & 0 \\ (1, 4, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  2 2 & 0 \\ (1, 4, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  1 2 & 0 \end{matrix}

210

\begin{matrix}(1, 4, 5, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  1 4  2 3 & 0 \\ (1, 4, 5, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  2 3 & 0 \\ (1, 4, 5, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 4  2 3 & 0 \\ (1, 4, 5, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  1 3 & 0 \\ (1, 4, 5, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  2 3 & 0 \\ (1, 4, 5, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  1 3 & 0 \end{matrix}

211

\begin{matrix}(1, 4, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  1 4  2 4 & 0 \\ (1, 4, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  2 4 & 0 \\ (1, 4, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 4  2 4 & 0 \\ (1, 4, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  1 4 & 0 \\ (1, 4, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  2 4 & 0 \\ (1, 4, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  1 4 & 0 \end{matrix} \begin{matrix}(1, 4, 5, 5, 5) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  1 5 & 0 \\ (1, 4, 5, 5, 5) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  1 5 & 0 \end{matrix}

212

(1, 4, 5, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  2 2  0 ; (1, 4, 5, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  2 2  −p^{3}(p − 1) ; h(1, 4, 5, 6, 2) = p^{3} − p^{4} (1, 4, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  1 4  3 3  −p^{3}(p − 1) ; (1, 4, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  3 3  0 ; (1, 4, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  2 3  0 ; (1, 4, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  3 3  p^{4}(p − 1) ; (1, 4, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  2 3  0 ; h(1, 4, 5, 6, 3) = p^{3} − 2p^{4} + p^{5}

213

(1, 4, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  1 4  3 4  0

(1, 4, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  2 4  0

(1, 4, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 4  3 4  p^{4}(p − 1)

(1, 4, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  2 4 −p^{3}(p − 1)^{2}

cancel

(1, 4, 5, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  2  1 5  2 5  0

(1, 4, 5, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  2 5  −p^{4}(p − 1)

h(1, 4, 5, 6, 5) = p^{4} − p^{5}

(1, 4, 5, 7, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  3 3  p^{5}

h(1, 4, 5, 7, 3) = p^{5}

(1, 4, 5, 7, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  3 4 0

(1, 4, 5, 7, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  0 5  3 5  −p^{5}

h(1, 4, 5, 7, 5) = −p^{5}

(1, 4, 6, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 3  1 1 0

(1, 4, 6, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 3  1 2 0

(1, 4, 6, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 3  1 3 0

(1, 4, 6, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  1 1 0

(1, 4, 6, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  2 3  2 2 −p^{3}(p − 1)

(1, 4, 6, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 3  2 2  0

(1, 4, 6, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  1 2  0

cancel

(1, 4, 6, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  2 3  2 3  p^{3}(p − 1)

(1, 4, 6, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  2 3  2 3 −p^{3}(p − 1)

(1, 4, 6, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 3  2 3  0

(1, 4, 6, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  1 3  0

cancel

(1, 4, 6, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  1 4 0

(1, 4, 6, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  1 1 0

(1, 4, 6, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  2 4  2 2  p^{3}(p − 1)

(1, 4, 6, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  2 4  2 2 −p^{3}(p − 1)

(1, 4, 6, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  2 2  0

(1, 4, 6, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  1 2  0

cancel

\begin{matrix}(1, 4, 6, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  2 4  2 3 & 0 \\ (1, 4, 6, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  2 4  2 3 & 0 \\ (1, 4, 6, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  2 3 & 0 \\ (1, 4, 6, 5, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  1 3 & 0 \end{matrix}

(1, 4, 6, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  2 4  2 4  p^{3}(p − 1)

(1, 4, 6, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  2 4  0

(1, 4, 6, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  1 4  0

cancel

(1, 4, 6, 5, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  1 5 0

(1, 4, 6, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  2 2 0

(1, 4, 6, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  2 4  3 3  p^{3}(p − 1)

(1, 4, 6, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  3 3  0

(1, 4, 6, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  2 3  0

cancel

(1, 4, 6, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 4  3  2  1 4  3  2 4  3 4 −p^{3}(p − 1)

(1, 4, 6, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 4  3  2 4  3 4  p^{3}(p − 1)

(1, 4, 6, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 4  3 4  0

(1, 4, 6, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  2 4  0

cancel

(1, 4, 6, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  2 5 0

(1, 4, 6, 7, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  3 3 0

(1, 4, 6, 7, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  3 4 0

(1, 4, 6, 7, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  1 5  3 5 0

(1, 4, 7, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 3  2 2  −p^{4}

h(1, 4, 7, 4, 2) = −p^{4}

(1, 4, 7, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 3  2 3  −p^{4}

h(1, 4, 7, 4, 3) = −p^{4}

(1, 4, 7, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 4  2 2 0

(1, 4, 7, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 4  2 3 0

(1, 4, 7, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 4  2 4 0

h(1, 4, 7, 6, 2) = p^{4}

(1, 4, 7, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 4  3 3  −p^{4}(p − 1)

(1, 4, 7, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 5  2 3  0

h(1, 4, 7, 6, 3) = p^{4} − p^{5}

(1, 4, 7, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 4  3 4 −p^{4}(p − 1)

(1, 4, 7, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 5  2 4  p^{4}(p − 1)

cancel

(1, 4, 7, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 5  2 5  p^{5}

h(1, 4, 7, 6, 5) = p^{5}

(1, 4, 7, 7, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 5  3 3  −p^{5}

h(1, 4, 7, 7, 3) = −p^{5}

(1, 4, 7, 7, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  0 5  3  2 5  3 4 0

h(1, 4, 7, 7, 5) = p^{5}

(1, 5, 3, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 3  2  1 2  1 1  −p^{3}

h(1, 5, 3, 2, 1) = −p^{3}

(1, 5, 3, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 3  2  1 2  1 2  −p^{3}

h(1, 5, 3, 2, 2) = −p^{3}

(1, 5, 3, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 3  2  1 3  1 1  −p^{3}

h(1, 5, 3, 3, 1) = −p^{3}

(1, 5, 3, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 3  2  1 3  1 2 0

(1, 5, 3, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 3  2  1 3  1 3  p^{3}

h(1, 5, 3, 3, 3) = p^{3}

(1, 5, 3, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 3  2  1 3  2 2  p^{3}

h(1, 5, 3, 4, 2) = p^{3}

h(1, 5, 3, 4, 3) = p^{3}

(1, 5, 4, 2, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 2  1 1 0

(1, 5, 4, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 2  1 2 0

(1, 5, 4, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 3  1 1 0

(1, 5, 4, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 3  1 2 0

(1, 5, 4, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 3  1 3 0

(1, 5, 4, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 4  1 1 0

\begin{matrix}(1, 5, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 3  2 2 & 0 \\ (1, 5, 4, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(1, 5, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 3  2 3 & 0 \\ (1, 5, 4, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 4  1 3 & 0 \end{matrix}

(1, 5, 4, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 4  1 4 0

(1, 5, 4, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 4  2 2 0

(1, 5, 4, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 4  2 3 0

(1, 5, 4, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  2  1 4  2 4 0

h(1, 5, 5, 2, 1) = p^{3}

(1, 5, 5, 2, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 2  1 2  p^{3}

h(1, 5, 5, 2, 2) = p^{3}

(1, 5, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 3  1 1  −p^{3}(p − 1)

(1, 5, 5, 3, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 3  1 1  0

h(1, 5, 5, 3, 1) = p^{3} − p^{4}

\begin{matrix}(1, 5, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 3  1 2 & 0 \\ (1, 5, 5, 3, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 3  1 2 & 0 \end{matrix}

(1, 5, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 3  1 3  p^{3}(p − 1)

(1, 5, 5, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 3  1 3  0

h(1, 5, 5, 3, 3) = −p^{3} + p^{4}

(1, 5, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  1 1 −p^{3}(p − 1) ; (1, 5, 5, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 4  1 1  p^{3}(p − 1) ; cancel (1, 5, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 3  2 2  0 ; (1, 5, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  1 2  0 ; (1, 5, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 3  2 2  p^{3}(p − 1) ; (1, 5, 5, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 4  1 2  0 ; h(1, 5, 5, 4, 2) = −p^{3} + p^{4}

226

(1, 5, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  1 3  −p^{3}(p − 1)^{2}

(1, 5, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 3  2 3  p^{3}(p − 1)

(1, 5, 5, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 4  1 3  p^{3}(p − 1)^{2}

h(1, 5, 5, 4, 3) = −p^{3} + p^{4}

(1, 5, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  1 4 −p^{4}(p − 1)

(1, 5, 5, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 4  1 4  p^{4}(p − 1)

cancel

(1, 5, 5, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 5  1 1  p^{4}

h(1, 5, 5, 5, 1) = p^{4}

\begin{matrix}(1, 5, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  2 2 & 0 \\ (1, 5, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 4  2 2 & 0 \\ (1, 5, 5, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 5  1 2 & 0 \end{matrix}

(1, 5, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  2 3  0

(1, 5, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 4  2 3  0

(1, 5, 5, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 5  1 3  p^{4}(p − 1)

h(1, 5, 5, 5, 3) = −p^{4} + p^{5}

\begin{matrix}(1, 5, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  2 4 & 0 \\ (1, 5, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 4  2 4 & 0 \\ (1, 5, 5, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 5  1 4 & 0 \end{matrix}

h(1, 5, 5, 5, 5) = −p^{5}

(1, 5, 5, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 5  2 2  −p^{4}

h(1, 5, 5, 6, 2) = −p^{4}

(1, 5, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  3 3  p^{4}(p − 1)

(1, 5, 5, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 5  2 3  0

h(1, 5, 5, 6, 3) = −p^{4} + p^{5}

(1, 5, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  1 4  3 4  p^{4}(p − 1)

(1, 5, 5, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 5  2 4 −p^{4}(p − 1)

cancel

(1, 5, 5, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  2  1 5  2 5  −p^{5}

h(1, 5, 5, 6, 5) = −p^{5}

h(1, 5, 6, 3, 1) = −p^{4}

(1, 5, 6, 3, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 3  1 2 0

(1, 5, 6, 3, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 3  1 3  p^{4}

h(1, 5, 6, 3, 3) = p^{4}

(1, 5, 6, 4, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  1 1 0

\begin{matrix}(1, 5, 6, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  2 3  2 2 & 0 \\ (1, 5, 6, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 3  2 2 & 0 \\ (1, 5, 6, 4, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(1, 5, 6, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  2 3  2 3 & 0 \\ (1, 5, 6, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 3  2 3 & 0 \\ (1, 5, 6, 4, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  1 3 & 0 \end{matrix}

(1, 5, 6, 4, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  1 4 0

(1, 5, 6, 5, 1) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  1 1  p^{4}

h(1, 5, 6, 5, 1) = p^{4}

\begin{matrix}(1, 5, 6, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  2 4  2 2 & 0 \\ (1, 5, 6, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  2 2 & 0 \\ (1, 5, 6, 5, 2) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  1 2 & 0 \end{matrix}

(1, 5, 6, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  2 3  0

(1, 5, 6, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  1 3  p^{4}(p − 1)

h(1, 5, 6, 5, 3) = −p^{4} + p^{5}

\begin{matrix}(1, 5, 6, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  2 4  2 4 & 0 \\ (1, 5, 6, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  2 4 & 0 \\ (1, 5, 6, 5, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  1 4 & 0 \end{matrix}

(1, 5, 6, 5, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  1 5  −p^{5}

h(1, 5, 6, 5, 5) = −p^{5}

(1, 5, 6, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  2 2 0

\begin{matrix}(1, 5, 6, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  2 4  3 3 & 0 \\ (1, 5, 6, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  3 3 & 0 \\ (1, 5, 6, 6, 3) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  2 3 & 0 \end{matrix}

\begin{matrix}(1, 5, 6, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 4  3  2 4  3 4 & 0 \\ (1, 5, 6, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 4  3 4 & 0 \\ (1, 5, 6, 6, 4) & 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  2 4 & 0 \end{matrix}

(1, 5, 6, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  2 5 0

(1, 5, 6, 7, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  3 3  −p^{5}

h(1, 5, 6, 7, 3) = −p^{5}

(1, 5, 6, 7, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  1 5  3 4 0

h(1, 5, 6, 7, 5) = p^{5}

(1, 5, 7, 4, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 3  2 2  −p^{4}

h(1, 5, 7, 4, 2) = −p^{4}

(1, 5, 7, 4, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 3  2 3  −p^{4}

h(1, 5, 7, 4, 3) = −p^{4}

(1, 5, 7, 5, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 4  2 2 0

(1, 5, 7, 5, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 4  2 3 0

(1, 5, 7, 5, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 4  2 4 0

(1, 5, 7, 6, 2) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 5  2 2  p^{4}

h(1, 5, 7, 6, 2) = p^{4}

(1, 5, 7, 6, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 5  2 3  0

h(1, 5, 7, 6, 3) = p^{4} − p^{5}

(1, 5, 7, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 4  3 4 −p^{4}(p − 1)

(1, 5, 7, 6, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 5  2 4  p^{4}(p − 1)

cancel

(1, 5, 7, 6, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 5  2 5  p^{5}

h(1, 5, 7, 6, 5) = p^{5}

(1, 5, 7, 7, 3) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 5  3 3  −p^{5}

h(1, 5, 7, 7, 3) = −p^{5}

(1, 5, 7, 7, 4) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 5  3 4 0

(1, 5, 7, 7, 5) 5  4  3  2  1  0 5  3  2  1  0 5  3  2  1 5  3  2 5  3 5  p^{5}

h(1, 5, 7, 7, 5) = p^{5}

h(2, 1, 0, 0, 0) = −1

(2, 1, 0, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 2  1  0 1  0 1  −1

h(2, 1, 0, 0, 1) = −1

(2, 1, 0, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 2  1  0 2  0 0  −1

h(2, 1, 0, 1, 0) = −1

(2, 1, 0, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 2  1  0 2  0 1 0

(2, 1, 0, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 2  1  0 2  0 2  1

h(2, 1, 0, 1, 2) = 1

(2, 1, 0, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 2  1  0 2  1 1  1

h(2, 1, 0, 2, 1) = 1

(2, 1, 0, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 2  1  0 2  1 2  1

h(2, 1, 0, 2, 2) = 1

(2, 1, 1, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 1  0 0 0

(2, 1, 1, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 1  0 1 0

(2, 1, 1, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 2  0 0 0

(2, 1, 1, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 2  0 1 0

(2, 1, 1, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 2  0 2 0

(2, 1, 1, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 3  0 0 0

\begin{matrix}(2, 1, 1, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 2  1 1 & 0 \\ (2, 1, 1, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(2, 1, 1, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 2  1 2 & 0 \\ (2, 1, 1, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 3  0 2 & 0 \end{matrix}

(2, 1, 1, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 3  0 3 0

(2, 1, 1, 3, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 3  1 1 0

(2, 1, 1, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 3  1 2 0

(2, 1, 1, 3, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  1  0 3  1 3 0

(2, 1, 2, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 1  0 0  1

h(2, 1, 2, 0, 0) = 1

(2, 1, 2, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 1  0 1  1

h(2, 1, 2, 0, 1) = 1

(2, 1, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 2  0 0  −(p − 1)
(2, 1, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 2  0 0  0

h(2, 1, 2, 1, 0) = 1 − p

\begin{matrix}(2, 1, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 2  0 1 & 0 \\ (2, 1, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 2  0 1 & 0 \end{matrix}
(2, 1, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 2  0 2  (p − 1)
(2, 1, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 2  0 2  0

h(2, 1, 2, 1, 2) = −1 + p

(2, 1, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 3  0 0 −(p − 1)
(2, 1, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 3  0 0  (p − 1)

cancel

(2, 1, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 2  1 1  0 ; (2, 1, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 3  0 1  0 ; (2, 1, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 2  1 1  (p − 1) ; (2, 1, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 3  0 1  0 ; h(2, 1, 2, 2, 1) = −1 + p (2, 1, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 2  1 2  0 ; (2, 1, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 3  0 2  −(p − 1)^{2} ; (2, 1, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 2  1 2  (p − 1) ; (2, 1, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 3  0 2  (p − 1)^{2} ; h(2, 1, 2, 2, 2) = −1 + p

240

(2, 1, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 3  0 3  p(p − 1)

cancel

(2, 1, 2, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  0 0  p

h(2, 1, 2, 3, 0) = p

\begin{matrix}(2, 1, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 3  1 1 & 0 \\ (2, 1, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 3  1 1 & 0 \\ (2, 1, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  0 1 & 0 \end{matrix}

(2, 1, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 3  1 2  0

(2, 1, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  0 2  p(p − 1)

h(2, 1, 2, 3, 2) = −p + p^{2}

\begin{matrix}(2, 1, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 3  1 3 & 0 \\ (2, 1, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 3  1 3 & 0 \\ (2, 1, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  0 3 & 0 \end{matrix}

(2, 1, 2, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  0 4  −p^{2}

h(2, 1, 2, 3, 4) = −p^{2}

(2, 1, 2, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  1 1  −p

h(2, 1, 2, 4, 1) = −p

(2, 1, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  1 2  0

h(2, 1, 2, 4, 2) = −p + p^{2}

(2, 1, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  0 3  2 3  p(p − 1)

(2, 1, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  1 3 −p(p − 1)

cancel

(2, 1, 2, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  1  0 4  1 4  −p^{2}

h(2, 1, 2, 4, 4) = −p^{2}

(2, 1, 3, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 2  0 0  −p

h(2, 1, 3, 1, 0) = −p

(2, 1, 3, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 2  0 1 0

(2, 1, 3, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 2  0 2  p

h(2, 1, 3, 1, 2) = p

(2, 1, 3, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  0 0 0

\begin{matrix}(2, 1, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  1 2  1 1 & 0 \\ (2, 1, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 2  1 1 & 0 \\ (2, 1, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(2, 1, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  1 2  1 2 & 0 \\ (2, 1, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 2  1 2 & 0 \\ (2, 1, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  0 2 & 0 \end{matrix}

(2, 1, 3, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  0 3 0

(2, 1, 3, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  0 0  p

h(2, 1, 3, 3, 0) = p

\begin{matrix}(2, 1, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  1 3  1 1 & 0 \\ (2, 1, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  1 1 & 0 \\ (2, 1, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  0 1 & 0 \end{matrix}

(2, 1, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  1 3  1 2  0

(2, 1, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  1 2  0

(2, 1, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  0 2  p(p − 1)

h(2, 1, 3, 3, 2) = −p + p^{2}

\begin{matrix}(2, 1, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  1 3  1 3 & 0 \\ (2, 1, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  1 3 & 0 \\ (2, 1, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  0 3 & 0 \end{matrix}

h(2, 1, 3, 3, 4) = −p^{2}

(2, 1, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  1 1 0

\begin{matrix}(2, 1, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  1 3  2 2 & 0 \\ (2, 1, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  2 2 & 0 \\ (2, 1, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(2, 1, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 3  2  1 3  2 3 & 0 \\ (2, 1, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 3  2 3 & 0 \\ (2, 1, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  1 3 & 0 \end{matrix}

(2, 1, 3, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  1 4 0

h(2, 1, 3, 5, 2) = −p^{2}

(2, 1, 3, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  2 3 0

(2, 1, 3, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  0 4  2 4  p^{2}

h(2, 1, 3, 5, 4) = p^{2}

(2, 1, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 2  1 1  −p

h(2, 1, 4, 2, 1) = −p

(2, 1, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 2  1 2  −p

h(2, 1, 4, 2, 2) = −p

(2, 1, 4, 3, 1) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 3  1 1 0

(2, 1, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 3  1 2 0

(2, 1, 4, 3, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 3  1 3 0

h(2, 1, 4, 4, 1) = p

(2, 1, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 3  2 2  −p(p − 1)

(2, 1, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 4  1 2  0

h(2, 1, 4, 4, 2) = p − p^{2}

(2, 1, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 3  2 3 −p(p − 1)

(2, 1, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 4  1 3  p(p − 1)

cancel

(2, 1, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 4  1 4  p^{2}

h(2, 1, 4, 4, 4) = p^{2}

(2, 1, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 4  2 2  −p^{2}

h(2, 1, 4, 5, 2) = −p^{2}

(2, 1, 4, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 4  2  1  0 4  2  1 4  2 3 0

h(2, 1, 4, 5, 4) = p^{2}

(2, 2, 0, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 2  1  0 1  0 0  −1

h(2, 2, 0, 0, 0) = −1

(2, 2, 0, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 2  1  0 1  0 1  −1

h(2, 2, 0, 0, 1) = −1

(2, 2, 0, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 2  1  0 2  0 0  −1

h(2, 2, 0, 1, 0) = −1

(2, 2, 0, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 2  1  0 2  0 1 0

(2, 2, 0, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 2  1  0 2  0 2  1

h(2, 2, 0, 1, 2) = 1

(2, 2, 0, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 2  1  0 2  1 1  1

h(2, 2, 0, 2, 1) = 1

h(2, 2, 0, 2, 2) = 1

\begin{matrix}(2, 2, 1, 0, 0) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 1  0 0 & 0 \\ (2, 2, 1, 0, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 1  0 0 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 0, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 1  0 1 & 0 \\ (2, 2, 1, 0, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 1  0 1 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 1, 0) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 2  0 0 & 0 \\ (2, 2, 1, 1, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 2  0 1 & 0 \\ (2, 2, 1, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 1, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 2  0 2 & 0 \\ (2, 2, 1, 1, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 2  0 2 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 3  0 0 & 0 \\ (2, 2, 1, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 3  0 0 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 2  1 1 & 0 \\ (2, 2, 1, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 3  0 1 & 0 \\ (2, 2, 1, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 2  1 1 & 0 \\ (2, 2, 1, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 2  1 2 & 0 \\ (2, 2, 1, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 3  0 2 & 0 \\ (2, 2, 1, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 2  1 2 & 0 \\ (2, 2, 1, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 3  0 2 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 3  0 3 & 0 \\ (2, 2, 1, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 3  0 3 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 3  1 1 & 0 \\ (2, 2, 1, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 3  1 1 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 3  1 2 & 0 \\ (2, 2, 1, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 3  1 2 & 0 \end{matrix}

\begin{matrix}(2, 2, 1, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  1  0 3  1 3 & 0 \\ (2, 2, 1, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  1  0 3  1 3 & 0 \end{matrix}

(2, 2, 2, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 1  0 0  0

(2, 2, 2, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 1  0 0  −(p − 1)

h(2, 2, 2, 0, 0) = 1 − p

(2, 2, 2, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 1  0 1  0

(2, 2, 2, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 1  0 1  −(p − 1)

h(2, 2, 2, 0, 1) = 1 − p

(2, 2, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 2  0 0  0 ; (2, 2, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 2  0 0  0 ; (2, 2, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 2  0 0  −(p − 1) ; (2, 2, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 2  0 0  0 ; h(2, 2, 2, 1, 0) = 1 − p \begin{matrix}(2, 2, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 2  0 1 & 0 \\ (2, 2, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 2  0 1 & 0 \\ (2, 2, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 2  0 1 & 0 \\ (2, 2, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 2  0 1 & 0 \end{matrix}

254

(2, 2, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 2  0 2  0 ; (2, 2, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 2  0 2  0 ; (2, 2, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 2  0 2  (p − 1) ; (2, 2, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 2  0 2  0 ; h(2, 2, 2, 1, 2) = −1 + p (2, 2, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 3  0 0  0 ; (2, 2, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 3  0 0  0 ; (2, 2, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  0 0  −(p − 1) ; (2, 2, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 3  0 0  −(p − 1)^{2} ; h(2, 2, 2, 2, 0) = p − p^{2}

255

(2, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 3  0 1  0

(2, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 2  1 1  0

(2, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 3  0 1  0

(2, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 2  1 1  0

(2, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  0 1  0

(2, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 2  1 1  −(p − 1)^{2}

(2, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 3  0 1  0

h(2, 2, 2, 2, 1) = −1 + 2p − p^{2}

(2, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 3  0 2  0

(2, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 2  1 2  0

(2, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 3  0 2  0

(2, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 2  1 2  0

(2, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  0 2  −(p − 1)^{2}

(2, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 2  1 2  −(p − 1)^{2}

(2, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 3  0 2  −(p − 1)^{3}

h(2, 2, 2, 2, 2) = −1 + p + p^{2} − p^{3}

(2, 2, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 3  0 3  0 ; (2, 2, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 3  0 3  0 ; (2, 2, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  0 3  −p(p − 1) ; (2, 2, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 3  0 3  −p(p − 1)^{2} ; h(2, 2, 2, 2, 3) = p^{2} − p^{3} (2, 2, 2, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  0 0  0 ; (2, 2, 2, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  0 0  −p(p − 1) ; h(2, 2, 2, 3, 0) = p − p^{2}

258

\begin{matrix}(2, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 3  1 1 & 0 \\ (2, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 3  1 1 & 0 \\ (2, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  0 1 & 0 \\ (2, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  1 1 & 0 \\ (2, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 3  1 1 & 0 \\ (2, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  0 1 & 0 \end{matrix}

259

(2, 2, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 3  1 2  0

(2, 2, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  0 2  0

(2, 2, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  1 2  0

(2, 2, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 3  1 2  0

(2, 2, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  0 2  −p(p − 1)^{2}

h(2, 2, 2, 3, 2) = −p + 2p^{2} − p^{3}

\begin{matrix}(2, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 3  1 3 & 0 \\ (2, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 3  1 3 & 0 \\ (2, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  0 3 & 0 \\ (2, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  1 3 & 0 \\ (2, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 3  1 3 & 0 \\ (2, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  0 3 & 0 \end{matrix} (2, 2, 2, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  0 4  0 ; (2, 2, 2, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  0 4  p^{2}(p − 1) ; h(2, 2, 2, 3, 4) = −p^{2} + p^{3}

261

(2, 2, 2, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  1 1  0 ; (2, 2, 2, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  1 1  p(p − 1) ; h(2, 2, 2, 4, 1) = −p + p^{2} (2, 2, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  0 3  2 2  0 ; (2, 2, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  1 2  0 ; (2, 2, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  2 2  p(p − 1) ; (2, 2, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  1 2  0 ; h(2, 2, 2, 4, 2) = −p + p^{2}

262

(2, 2, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  1 3  0

(2, 2, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  0 3  2 3  p(p − 1)

(2, 2, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  1 3  p(p − 1)^{2}

h(2, 2, 2, 4, 3) = −p^{2} + p^{3}

(2, 2, 2, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  1  0 4  1 4  0

(2, 2, 2, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  1  0 4  1 4  p^{2}(p − 1)

h(2, 2, 2, 4, 4) = −p^{2} + p^{3}

(2, 2, 3, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 1  0 0  −p

h(2, 2, 3, 0, 0) = −p

(2, 2, 3, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 1  0 1  −p

h(2, 2, 3, 0, 1) = −p

\begin{matrix}(2, 2, 3, 1, 0) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 2  0 0 & 0 \\ (2, 2, 3, 1, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 2  0 0 & 0 \\ (2, 2, 3, 1, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(2, 2, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 2  0 1 & 0 \\ (2, 2, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 2  0 1 & 0 \\ (2, 2, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(2, 2, 3, 1, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 2  0 2 & 0 \\ (2, 2, 3, 1, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 2  0 2 & 0 \\ (2, 2, 3, 1, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 2  0 2 & 0 \end{matrix}

(2, 2, 3, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  0 0  0

(2, 2, 3, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 3  0 0  −p(p − 1)

h(2, 2, 3, 2, 0) = p − p^{2}

(2, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 2  1 1  0

(2, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 3  0 1  0

(2, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  1 2  1 1  0

(2, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 2  1 1  0

(2, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  0 1  0

(2, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 2  1 1  −p(p − 1)

(2, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 3  0 1  0

h(2, 2, 3, 2, 1) = p − p^{2}

(2, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 2  1 2  0

(2, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 3  0 2  0

(2, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  1 2  1 2  0

(2, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 2  1 2  0

(2, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  0 2  0

(2, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 2  1 2  −p(p − 1)

(2, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 3  0 2  −p(p − 1)^{2}

h(2, 2, 3, 2, 2) = p^{2} − p^{3}

(2, 2, 3, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 3  0 3  0 ; (2, 2, 3, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  0 3  0 ; (2, 2, 3, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 3  0 3  −p^{2}(p − 1) ; h(2, 2, 3, 2, 3) = p^{2} − p^{3} \begin{matrix}(2, 2, 3, 3, 0) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  0 0 & 0 \\ (2, 2, 3, 3, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  0 0 & 0 \\ (2, 2, 3, 3, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  0 0 & 0 \end{matrix}

268

\begin{matrix}(2, 2, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  1 3  1 1 & 0 \\ (2, 2, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 3  1 1 & 0 \\ (2, 2, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  0 1 & 0 \\ (2, 2, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  1 3  1 1 & 0 \\ (2, 2, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  1 1 & 0 \\ (2, 2, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  0 1 & 0 \\ (2, 2, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 3  1 1 & 0 \\ (2, 2, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  0 1 & 0 \end{matrix}

269

\begin{matrix}(2, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  1 3  1 2 & 0 \\ (2, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 3  1 2 & 0 \\ (2, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  0 2 & 0 \\ (2, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  1 3  1 2 & 0 \\ (2, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  1 2 & 0 \\ (2, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  0 2 & 0 \\ (2, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 3  1 2 & 0 \\ (2, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  0 2 & 0 \end{matrix}

270

\begin{matrix}(2, 2, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 3  2  1 3  1 3 & 0 \\ (2, 2, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 3  1 3 & 0 \\ (2, 2, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  0 3 & 0 \\ (2, 2, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  1 3  1 3 & 0 \\ (2, 2, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  1 3 & 0 \\ (2, 2, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  0 3 & 0 \\ (2, 2, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 3  1 3 & 0 \\ (2, 2, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  0 3 & 0 \end{matrix}

271

\begin{matrix}(2, 2, 3, 3, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  0 4 & 0 \\ (2, 2, 3, 3, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  0 4 & 0 \\ (2, 2, 3, 3, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  0 4 & 0 \end{matrix}

(2, 2, 3, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  0 0  p^{2}

h(2, 2, 3, 4, 0) = p^{2}

(2, 2, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  1 1  0

(2, 2, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  1 1  0

(2, 2, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  1 1  −p^{2}(p − 1)

(2, 2, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  0 1  0

h(2, 2, 3, 4, 1) = p^{2} − p^{3}

(2, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 3  2 2  0

(2, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  1 2  0

(2, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  1 3  2 2  0

(2, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  2 2  0

(2, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  1 2  0

(2, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  1 2  0

(2, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  0 2  p^{2}(p − 1)

h(2, 2, 3, 4, 2) = −p^{2} + p^{3}

(2, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 3  2 3  0

(2, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  1 3  0

(2, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 3  2  1 3  2 3  0

(2, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 3  2 3  0

(2, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  1 3  0

(2, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  1 3  −p^{2}(p − 1)^{2}

(2, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  0 3  0

h(2, 2, 3, 4, 3) = −p^{2} + 2p^{3} − p^{4}

(2, 2, 3, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  1 4  0

(2, 2, 3, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 4  1 4 −p^{3}(p − 1)

(2, 2, 3, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  0 4  p^{3}(p − 1)

cancel

(2, 2, 3, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  0 5  p^{4}

h(2, 2, 3, 4, 5) = p^{4}

(2, 2, 3, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  1 1  −p^{3}

h(2, 2, 3, 5, 1) = −p^{3}

\begin{matrix}(2, 2, 3, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  2 2 & 0 \\ (2, 2, 3, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  2 2 & 0 \\ (2, 2, 3, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  1 2 & 0 \end{matrix}

(2, 2, 3, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  2 3  0

(2, 2, 3, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  2 3  0

(2, 2, 3, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  1 3  −p^{3}(p − 1)

h(2, 2, 3, 5, 3) = p^{3} − p^{4}

\begin{matrix}(2, 2, 3, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  0 4  2 4 & 0 \\ (2, 2, 3, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  0 4  2 4 & 0 \\ (2, 2, 3, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  1  0 5  1 4 & 0 \end{matrix}

h(2, 2, 3, 5, 5) = p^{4}

(2, 2, 4, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 2  0 0  p

h(2, 2, 4, 1, 0) = p

(2, 2, 4, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 2  0 1 0

(2, 2, 4, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 2  0 2  −p

h(2, 2, 4, 1, 2) = −p

\begin{matrix}(2, 2, 4, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  0 0 & 0 \\ (2, 2, 4, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  0 0 & 0 \end{matrix}

(2, 2, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  0 1  0

(2, 2, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 2  1 1  p(p − 1)

(2, 2, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 2  1 1  0

(2, 2, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  0 1  0

h(2, 2, 4, 2, 1) = −p + p^{2}

(2, 2, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 2  1 2  0 ; (2, 2, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  0 2  0 ; (2, 2, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 2  1 2  p(p − 1) ; (2, 2, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 2  1 2  0 ; (2, 2, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  0 2  0 ; h(2, 2, 4, 2, 2) = −p + p^{2} \begin{matrix}(2, 2, 4, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  0 3 & 0 \\ (2, 2, 4, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  0 3 & 0 \end{matrix}

279

(2, 2, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  0 0  0 ; (2, 2, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  0 0  p(p − 1) ; h(2, 2, 4, 3, 0) = −p + p^{2} \begin{matrix}(2, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 3  1 1 & 0 \\ (2, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  1 1 & 0 \\ (2, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  0 1 & 0 \\ (2, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 3  1 1 & 0 \\ (2, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  1 1 & 0 \\ (2, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  0 1 & 0 \end{matrix}

280

(2, 2, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  1 2  0

(2, 2, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  0 2  0

(2, 2, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 3  1 2  0

(2, 2, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  1 2  0

(2, 2, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  0 2  p(p − 1)^{2}

h(2, 2, 4, 3, 2) = p − 2p^{2} + p^{3}

\begin{matrix}(2, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 3  1 3 & 0 \\ (2, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  1 3 & 0 \\ (2, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  0 3 & 0 \\ (2, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 3  1 3 & 0 \\ (2, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  1 3 & 0 \\ (2, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  0 3 & 0 \end{matrix} (2, 2, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  0 4  0 ; (2, 2, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  0 4  −p^{2}(p − 1) ; h(2, 2, 4, 3, 4) = p^{2} − p^{3}

282

(2, 2, 4, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  0 0  p^{2} ; h(2, 2, 4, 4, 0) = p^{2} (2, 2, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 4  1 1  0 ; (2, 2, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  1 1  0 ; (2, 2, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 4  1 1  −p(p − 1) ; (2, 2, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  1 1  0 ; (2, 2, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  0 1  0 ; h(2, 2, 4, 4, 1) = p − p^{2}

283

(2, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 4  1 2  0

(2, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  2 2  0

(2, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  1 2  0

(2, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 3  2 2  p(p − 1)^{2}

(2, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 4  1 2  0

(2, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  2 2  0

(2, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  1 2  0

(2, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  0 2  p^{2}(p − 1)

h(2, 2, 4, 4, 2) = p − 3p^{2} + 2p^{3}

(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 3  2 3  0
(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 4  1 3  0
(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 3  2 3  0
(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  1 3  0
(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 3  2 3  p(p − 1)^{2}
(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 4  1 3 −p(p − 1)^{2}
(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 3  2 3  0
(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  1 3  0
(2, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  0 3  0

cancel

(2, 2, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  1 4  0

(2, 2, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 4  1 4  −p^{2}(p − 1)

(2, 2, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  1 4  0

(2, 2, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  0 4  p^{3}(p − 1)

h(2, 2, 4, 4, 4) = p^{2} − 2p^{3} + p^{4}

(2, 2, 4, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  0 5  p^{4}

h(2, 2, 4, 4, 5) = p^{4}

(2, 2, 4, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  1 1 0

(2, 2, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 4  2 2  0
(2, 2, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  2 2  0
(2, 2, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 4  2 2  p^{2}(p − 1)
(2, 2, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  2 2 −p^{2}(p − 1)
(2, 2, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  1 2  0

cancel

\begin{matrix}(2, 2, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  2  1 4  2 3 & 0 \\ (2, 2, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  2 3 & 0 \\ (2, 2, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 4  2 3 & 0 \\ (2, 2, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  2 3 & 0 \\ (2, 2, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  1 3 & 0 \end{matrix}

288

(2, 2, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  2 4  0

(2, 2, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 4  2  1 4  2 4 −p^{2}(p − 1)

(2, 2, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 4  2 4  p^{2}(p − 1)

(2, 2, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  1 4  0

cancel

(2, 2, 4, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  1 5 0

(2, 2, 4, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  2 2  −p^{3}

h(2, 2, 4, 6, 2) = −p^{3}

\begin{matrix}(2, 2, 4, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  3 3 & 0 \\ (2, 2, 4, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  2 3 & 0 \end{matrix}

(2, 2, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  0 4  3 4  0

(2, 2, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  2 4  −p^{3}(p − 1)

h(2, 2, 4, 6, 4) = p^{3} − p^{4}

(2, 2, 4, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  0 5  2 5  −p^{4}

h(2, 2, 4, 6, 5) = −p^{4}

(2, 2, 5, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 2  1 1  p^{2}

h(2, 2, 5, 2, 1) = p^{2}

(2, 2, 5, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 2  1 2  p^{2}

h(2, 2, 5, 2, 2) = p^{2}

\begin{matrix}(2, 2, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 3  1 1 & 0 \\ (2, 2, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 3  1 1 & 0 \end{matrix}

\begin{matrix}(2, 2, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 3  1 2 & 0 \\ (2, 2, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 3  1 2 & 0 \end{matrix}

\begin{matrix}(2, 2, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 3  1 3 & 0 \\ (2, 2, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 3  1 3 & 0 \end{matrix}

(2, 2, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 4  1 1  0

(2, 2, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 4  1 1  p^{2}(p − 1)

h(2, 2, 5, 4, 1) = −p^{2} + p^{3}

(2, 2, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 3  2 2  0 ; (2, 2, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 4  1 2  0 ; (2, 2, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 3  2 2  p^{2}(p − 1) ; (2, 2, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 4  1 2  0 ; h(2, 2, 5, 4, 2) = −p^{2} + p^{3} (2, 2, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 3  2 3  0 ; (2, 2, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 4  1 3  0 ; (2, 2, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 3  2 3  p^{2}(p − 1) ; (2, 2, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 4  1 3  p^{2}(p − 1)^{2} ; h(2, 2, 5, 4, 3) = −p^{3} + p^{4}

292

(2, 2, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 4  1 4  p^{3}(p − 1)

h(2, 2, 5, 4, 4) = −p^{3} + p^{4}

(2, 2, 5, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  1 1  p^{3}

h(2, 2, 5, 5, 1) = p^{3}

\begin{matrix}(2, 2, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 4  2 2 & 0 \\ (2, 2, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 4  2 2 & 0 \\ (2, 2, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  1 2 & 0 \end{matrix}

(2, 2, 5, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 4  2 3  0

(2, 2, 5, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  1 3  p^{3}(p − 1)

h(2, 2, 5, 5, 3) = −p^{3} + p^{4}

\begin{matrix}(2, 2, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 4  2 4 & 0 \\ (2, 2, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 4  2 4 & 0 \\ (2, 2, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  1 4 & 0 \end{matrix}

(2, 2, 5, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  1 5  −p^{4}

h(2, 2, 5, 5, 5) = −p^{4}

(2, 2, 5, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  2 2  −p^{3}

h(2, 2, 5, 6, 2) = −p^{3}

\begin{matrix}(2, 2, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 4  3 3 & 0 \\ (2, 2, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  2 3 & 0 \end{matrix}

(2, 2, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  1  0 4  3  1 4  3 4  0

(2, 2, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  2 4  −p^{3}(p − 1)

h(2, 2, 5, 6, 4) = p^{3} − p^{4}

(2, 2, 5, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  2  1  0 5  2  1 5  2 5  −p^{4}

h(2, 2, 5, 6, 5) = −p^{4}

(2, 3, 1, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 1  0 0 0

(2, 3, 1, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 1  0 1 0

(2, 3, 1, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 2  0 0 0

(2, 3, 1, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 2  0 1 0

(2, 3, 1, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 2  0 2 0

(2, 3, 1, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 3  0 0 0

\begin{matrix}(2, 3, 1, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 2  1 1 & 0 \\ (2, 3, 1, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(2, 3, 1, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 2  1 2 & 0 \\ (2, 3, 1, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 3  0 2 & 0 \end{matrix}

(2, 3, 1, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 3  0 3 0

(2, 3, 1, 3, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 3  1 1 0

(2, 3, 1, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 3  1 2 0

(2, 3, 1, 3, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  1  0 3  1 3 0

(2, 3, 2, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 1  0 0 0

(2, 3, 2, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 1  0 1 0

(2, 3, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 2  0 0  −p(p − 1)

(2, 3, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 2  0 0  0

(2, 3, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 2  0 0  0

h(2, 3, 2, 1, 0) = p − p^{2}

\begin{matrix}(2, 3, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 2  0 1 & 0 \\ (2, 3, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 2  0 1 & 0 \\ (2, 3, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 2  0 1 & 0 \end{matrix} (2, 3, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 2  0 2  p(p − 1) ; (2, 3, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 2  0 2  0 ; (2, 3, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 2  0 2  0 ; h(2, 3, 2, 1, 2) = −p + p^{2}

298

(2, 3, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 3  0 0  −p(p − 1) ; (2, 3, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  0 0  0 ; (2, 3, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 3  0 0  0 ; h(2, 3, 2, 2, 0) = p − p^{2} \begin{matrix}(2, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 2  1 1 & 0 \\ (2, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 3  0 1 & 0 \\ (2, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 2  1 1 & 0 \\ (2, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  0 1 & 0 \\ (2, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 2  1 1 & 0 \\ (2, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 3  0 1 & 0 \end{matrix}

299

(2, 3, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 3  0 2  −p(p − 1)^{2}

(2, 3, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 2  1 2  0

(2, 3, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  0 2  0

(2, 3, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 2  1 2  0

(2, 3, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 3  0 2  0

h(2, 3, 2, 2, 2) = −p + 2p^{2} − p^{3}

(2, 3, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  0 3  0

(2, 3, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 3  0 3  0

h(2, 3, 2, 2, 3) = p^{2} − p^{3}

(2, 3, 2, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  0 0 0

\begin{matrix}(2, 3, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 3  1 1 & 0 \\ (2, 3, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  1 1 & 0 \\ (2, 3, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 3  1 1 & 0 \\ (2, 3, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  0 1 & 0 \end{matrix}

\begin{matrix}(2, 3, 2, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 3  1 2 & 0 \\ (2, 3, 2, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  1 2 & 0 \\ (2, 3, 2, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 3  1 2 & 0 \\ (2, 3, 2, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  0 2 & 0 \end{matrix}

\begin{matrix}(2, 3, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 3  1 3 & 0 \\ (2, 3, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  1 3 & 0 \\ (2, 3, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 3  1 3 & 0 \\ (2, 3, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  0 3 & 0 \end{matrix}

(2, 3, 2, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  0 4 0

(2, 3, 2, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  1 1 0

(2, 3, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 3  2 2  p^{2}(p − 1)

(2, 3, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  2 2  0

(2, 3, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  1 2  0

h(2, 3, 2, 4, 2) = −p^{2} + p^{3}

(2, 3, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  0 3  2 3  p^{2}(p − 1)

(2, 3, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  0 3  2 3  0

(2, 3, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  1 3  0

h(2, 3, 2, 4, 3) = −p^{2} + p^{3}

(2, 3, 2, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  1  0 4  1 4 0

(2, 3, 3, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 1  0 0 0

(2, 3, 3, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 1  0 1 0

(2, 3, 3, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 2  0 0  −p(p − 1)

(2, 3, 3, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 2  0 0  0

(2, 3, 3, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 2  0 0  0

h(2, 3, 3, 1, 0) = p − p^{2}

\begin{matrix}(2, 3, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 2  0 1 & 0 \\ (2, 3, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 2  0 1 & 0 \\ (2, 3, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 2  0 1 & 0 \end{matrix}

(2, 3, 3, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 2  0 2  p(p − 1) ; (2, 3, 3, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 2  0 2  0 ; (2, 3, 3, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 2  0 2  0 ; h(2, 3, 3, 1, 2) = −p + p^{2} \begin{matrix}(2, 3, 3, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  0 0 & 0 \\ (2, 3, 3, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  0 0 & 0 \\ (2, 3, 3, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 3  0 0 & 0 \end{matrix}

305

\begin{matrix}(2, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  1 2  1 1 & 0 \\ (2, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 2  1 1 & 0 \\ (2, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  0 1 & 0 \\ (2, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  1 2  1 1 & 0 \\ (2, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 2  1 1 & 0 \\ (2, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  0 1 & 0 \\ (2, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 2  1 1 & 0 \\ (2, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 3  0 1 & 0 \end{matrix}

306

\begin{matrix}(2, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  1 2  1 2 & 0 \\ (2, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 2  1 2 & 0 \\ (2, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  0 2 & 0 \\ (2, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  1 2  1 2 & 0 \\ (2, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 2  1 2 & 0 \\ (2, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  0 2 & 0 \\ (2, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 2  1 2 & 0 \\ (2, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 3  0 2 & 0 \end{matrix}

307

\begin{matrix}(2, 3, 3, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  0 3 & 0 \\ (2, 3, 3, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  0 3 & 0 \\ (2, 3, 3, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 3  0 3 & 0 \end{matrix} (2, 3, 3, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  0 0  p(p − 1) ; (2, 3, 3, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  0 0  0 ; (2, 3, 3, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  0 0  0 ; h(2, 3, 3, 3, 0) = −p + p^{2}

308

\begin{matrix}(2, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  1 3  1 1 & 0 \\ (2, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  1 1 & 0 \\ (2, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  0 1 & 0 \\ (2, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  1 3  1 1 & 0 \\ (2, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  1 1 & 0 \\ (2, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  0 1 & 0 \\ (2, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 3  1 1 & 0 \\ (2, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  0 1 & 0 \end{matrix}

309

(2, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  1 2  0

(2, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  0 2  p(p − 1)^{2}

(2, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  1 3  1 2  0

(2, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  1 2  0

(2, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  0 2  0

(2, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 3  1 2  0

(2, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  0 2  0

h(2, 3, 3, 3, 2) = p − 2p^{2} + p^{3}

\begin{matrix}(2, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  1 3  1 3 & 0 \\ (2, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  1 3 & 0 \\ (2, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  0 3 & 0 \\ (2, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  1 3  1 3 & 0 \\ (2, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  1 3 & 0 \\ (2, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  0 3 & 0 \\ (2, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 3  1 3 & 0 \\ (2, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  0 3 & 0 \end{matrix}

311

(2, 3, 3, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  0 4  0

(2, 3, 3, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  0 4  0

h(2, 3, 3, 3, 4) = p^{2} − p^{3}

(2, 3, 3, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  0 0 0

\begin{matrix}(2, 3, 3, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  1 1 & 0 \\ (2, 3, 3, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  1 1 & 0 \\ (2, 3, 3, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  1 1 & 0 \\ (2, 3, 3, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  0 1 & 0 \end{matrix}

\begin{matrix}(2, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  1 3  2 2 & 0 \\ (2, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  2 2 & 0 \\ (2, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  1 2 & 0 \\ (2, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  1 3  2 2 & 0 \\ (2, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  2 2 & 0 \\ (2, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  1 2 & 0 \\ (2, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  1 2 & 0 \\ (2, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  0 2 & 0 \end{matrix}

313

\begin{matrix}(2, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 3  2  1 3  2 3 & 0 \\ (2, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 3  2 3 & 0 \\ (2, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  1 3 & 0 \\ (2, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 3  2  1 3  2 3 & 0 \\ (2, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 3  2 3 & 0 \\ (2, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  1 3 & 0 \\ (2, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  1 3 & 0 \\ (2, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  0 3 & 0 \end{matrix}

314

\begin{matrix}(2, 3, 3, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  1 4 & 0 \\ (2, 3, 3, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  1 4 & 0 \\ (2, 3, 3, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 4  1 4 & 0 \\ (2, 3, 3, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  0 4 & 0 \end{matrix}

(2, 3, 3, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  0 5 0

(2, 3, 3, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  1 1 0

(2, 3, 3, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  2 2  −p^{2}(p − 1)

(2, 3, 3, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  2 2  0

(2, 3, 3, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  1 2  0

h(2, 3, 3, 5, 2) = p^{2} − p^{3}

\begin{matrix}(2, 3, 3, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  2 3 & 0 \\ (2, 3, 3, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  2 3 & 0 \\ (2, 3, 3, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  1 3 & 0 \end{matrix}

(2, 3, 3, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  0 4  2 4  p^{2}(p − 1)

(2, 3, 3, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  0 4  2 4  0

(2, 3, 3, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  1 4  0

h(2, 3, 3, 5, 4) = −p^{2} + p^{3}

(2, 3, 3, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  1  0 5  1 5 0

(2, 3, 4, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 2  0 0 0

(2, 3, 4, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 2  0 1 0

(2, 3, 4, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 2  0 2 0 (2, 3, 4, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  0 0  p(p − 1) ; (2, 3, 4, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  0 0  0 ; (2, 3, 4, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  0 0  0 ; h(2, 3, 4, 2, 0) = −p + p^{2}

317

\begin{matrix}(2, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 2  1 1 & 0 \\ (2, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  0 1 & 0 \\ (2, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 2  1 1 & 0 \\ (2, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  0 1 & 0 \\ (2, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 2  1 1 & 0 \\ (2, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  0 1 & 0 \end{matrix}

318

(2, 3, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  0 2  p(p − 1)^{2}

(2, 3, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 2  1 2  0

(2, 3, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  0 2  0

(2, 3, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 2  1 2  0

(2, 3, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  0 2  0

h(2, 3, 4, 2, 2) = p − 2p^{2} + p^{3}

(2, 3, 4, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  0 3  p^{2}(p − 1) ; (2, 3, 4, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  0 3  0 ; (2, 3, 4, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  0 3  0 ; h(2, 3, 4, 2, 3) = −p^{2} + p^{3} (2, 3, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  0 0  p(p − 1) ; (2, 3, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  0 0  0 ; (2, 3, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  0 0  0 ; h(2, 3, 4, 3, 0) = −p + p^{2}

320

\begin{matrix}(2, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 3  1 1 & 0 \\ (2, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  1 1 & 0 \\ (2, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  0 1 & 0 \\ (2, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 3  1 1 & 0 \\ (2, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  1 1 & 0 \\ (2, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  0 1 & 0 \\ (2, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  1 1 & 0 \\ (2, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  0 1 & 0 \end{matrix}

321

(2, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  1 2  0

(2, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  0 2  p(p − 1)^{2}

(2, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 3  1 2  0

(2, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  1 2  0

(2, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  0 2  0

(2, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  1 2  0

(2, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  0 2  0

h(2, 3, 4, 3, 2) = p − 2p^{2} + p^{3}

\begin{matrix}(2, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 3  1 3 & 0 \\ (2, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  1 3 & 0 \\ (2, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  0 3 & 0 \\ (2, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 3  1 3 & 0 \\ (2, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  1 3 & 0 \\ (2, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  0 3 & 0 \\ (2, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  1 3 & 0 \\ (2, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  0 3 & 0 \end{matrix}

323

(2, 3, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  0 4  −p^{2}(p − 1) ; (2, 3, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  0 4  0 ; (2, 3, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  0 4  0 ; h(2, 3, 4, 3, 4) = p^{2} − p^{3} (2, 3, 4, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  0 0 0

324

\begin{matrix}(2, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 4  1 1 & 0 \\ (2, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  1 1 & 0 \\ (2, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 4  1 1 & 0 \\ (2, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  1 1 & 0 \\ (2, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  1 1 & 0 \\ (2, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  0 1 & 0 \end{matrix}

325

\begin{matrix}(2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 3  2 2 & 0 \\ (2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 4  1 2 & 0 \\ (2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  2 2 & p^{2}(p − 1)^{2} \\ (2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  1 2 & 0 \\ (2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 3  2 2 & 0 \\ (2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 4  1 2 & 0 \\ (2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  2 2 & 0 \\ (2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  1 2 & 0 \\ (2, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  2 2 & 0 \end{matrix}

326

(2, 3, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  0 2  0

h(2, 3, 4, 4, 2) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 3  2 3 & 0 \\ (2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 4  1 3 & 0 \\ (2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 3  2 3 & p^{2}(p − 1)^{2} \\ (2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  1 3 & 0 \\ (2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 3  2 3 & 0 \\ (2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 4  1 3 & 0 \\ (2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 3  2 3 & 0 \\ (2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  1 3 & 0 \\ (2, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 3  2 3 & 0 \end{matrix}

328

(2, 3, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  1 3  0 ; (2, 3, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  0 3  0 ; h(2, 3, 4, 4, 3) = p^{2} − 2p^{3} + p^{4} \begin{matrix}(2, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 4  1 4 & 0 \\ (2, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  1 4 & 0 \\ (2, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 4  1 4 & 0 \\ (2, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  1 4 & 0 \\ (2, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  1 4 & 0 \\ (2, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  0 4 & 0 \end{matrix}

329

(2, 3, 4, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  0 5 0

(2, 3, 4, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  1 1 0

(2, 3, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 4  2 2  0

(2, 3, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  2 2  p^{2}(p − 1)^{2}

(2, 3, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 4  2 2  0

(2, 3, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  2 2  0

(2, 3, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  2 2  0

(2, 3, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  1 2  0

h(2, 3, 4, 5, 2) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(2, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  2  1 4  2 3 & 0 \\ (2, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  2 3 & 0 \\ (2, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 4  2 3 & 0 \\ (2, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  2 3 & 0 \\ (2, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  2 3 & 0 \\ (2, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  1 3 & 0 \end{matrix}

331

(2, 3, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  2 4  −p^{2}(p − 1)^{2}

(2, 3, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  2  1 4  2 4  0

(2, 3, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  2 4  0

(2, 3, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 4  2 4  0

(2, 3, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  1 4  0

h(2, 3, 4, 5, 4) = −p^{2} + 2p^{3} − p^{4}

(2, 3, 4, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  1 5 0

(2, 3, 4, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  2 2 0

(2, 3, 4, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  3 3  0

(2, 3, 4, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  2 3  0

h(2, 3, 4, 6, 3) = p^{3} − p^{4}

(2, 3, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  0 4  3 4  −p^{3}(p − 1)

(2, 3, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  0 4  3 4  0

(2, 3, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  2 4  0

h(2, 3, 4, 6, 4) = p^{3} − p^{4}

(2, 3, 4, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  0 5  2 5 0

(2, 3, 5, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  0 0 0

\begin{matrix}(2, 3, 5, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 2  1 1 & 0 \\ (2, 3, 5, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(2, 3, 5, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 2  1 2 & 0 \\ (2, 3, 5, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  0 2 & 0 \end{matrix}

(2, 3, 5, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  0 3 0

(2, 3, 5, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  0 0 0

\begin{matrix}(2, 3, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 3  1 1 & 0 \\ (2, 3, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 3  1 1 & 0 \\ (2, 3, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 3  1 1 & 0 \\ (2, 3, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  1 1 & 0 \\ (2, 3, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  0 1 & 0 \end{matrix}

335

\begin{matrix}(2, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 3  1 2 & 0 \\ (2, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 3  1 2 & 0 \\ (2, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 3  1 2 & 0 \\ (2, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  1 2 & 0 \\ (2, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  0 2 & 0 \end{matrix}

336

\begin{matrix}(2, 3, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 3  1 3 & 0 \\ (2, 3, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 3  1 3 & 0 \\ (2, 3, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 3  1 3 & 0 \\ (2, 3, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  1 3 & 0 \\ (2, 3, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  0 3 & 0 \end{matrix}

(2, 3, 5, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  0 4 0

(2, 3, 5, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  0 0 0

\begin{matrix}(2, 3, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  1 1 & 0 \\ (2, 3, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  1 1 & 0 \\ (2, 3, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 4  1 1 & 0 \\ (2, 3, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  1 1 & 0 \\ (2, 3, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  0 1 & 0 \end{matrix}

338

\begin{matrix}(2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 3  2 2 & 0 \\ (2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  1 2 & 0 \\ (2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 3  2 2 & 0 \\ (2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  1 2 & 0 \\ (2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 3  2 2 & 0 \\ (2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 4  1 2 & 0 \\ (2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  2 2 & 0 \\ (2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  1 2 & 0 \\ (2, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  0 2 & 0 \end{matrix}

339

\begin{matrix}(2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 3  2 3 & 0 \\ (2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  1 3 & 0 \\ (2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 3  2 3 & 0 \\ (2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  1 3 & 0 \\ (2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 3  2 3 & 0 \\ (2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 4  1 3 & 0 \\ (2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 3  2 3 & 0 \\ (2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  1 3 & 0 \\ (2, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  0 3 & 0 \end{matrix}

340

\begin{matrix}(2, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  1 4 & 0 \\ (2, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  1 4 & 0 \\ (2, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 4  1 4 & 0 \\ (2, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  1 4 & 0 \\ (2, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  0 4 & 0 \end{matrix}

(2, 3, 5, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  0 5 0

\begin{matrix}(2, 3, 5, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  1 1 & 0 \\ (2, 3, 5, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  1 1 & 0 \end{matrix}

\begin{matrix}(2, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  2 2 & 0 \\ (2, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  2 2 & 0 \\ (2, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 4  2 2 & 0 \\ (2, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  1 2 & 0 \\ (2, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  2 2 & 0 \\ (2, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  1 2 & 0 \end{matrix}

342

\begin{matrix}(2, 3, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  2 3 & 0 \\ (2, 3, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  2 3 & 0 \\ (2, 3, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 4  2 3 & 0 \\ (2, 3, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  1 3 & 0 \\ (2, 3, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  2 3 & 0 \\ (2, 3, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  1 3 & 0 \end{matrix}

343

\begin{matrix}(2, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  2 4 & 0 \\ (2, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  2 4 & 0 \\ (2, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 4  2 4 & 0 \\ (2, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  1 4 & 0 \\ (2, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  2 4 & 0 \\ (2, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  1 4 & 0 \end{matrix} \begin{matrix}(2, 3, 5, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  1 5 & 0 \\ (2, 3, 5, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  1 5 & 0 \end{matrix}

344

\begin{matrix}(2, 3, 5, 6, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  2 2 & 0 \\ (2, 3, 5, 6, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  2 2 & 0 \end{matrix} \begin{matrix}(2, 3, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  3 3 & 0 \\ (2, 3, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  3 3 & 0 \\ (2, 3, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  2 3 & 0 \\ (2, 3, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  3 3 & 0 \\ (2, 3, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  2 3 & 0 \end{matrix}

345

\begin{matrix}(2, 3, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  1 4  3 4 & 0 \\ (2, 3, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 4  3  1 4  3 4 & 0 \\ (2, 3, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  2 4 & 0 \\ (2, 3, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 4  3 4 & 0 \\ (2, 3, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  2 4 & 0 \end{matrix}

\begin{matrix}(2, 3, 5, 6, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  2  1 5  2 5 & 0 \\ (2, 3, 5, 6, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  2 5 & 0 \end{matrix}

(2, 3, 5, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  3 3 0

(2, 3, 5, 7, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  3 4 0

(2, 3, 5, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  0 5  3 5 0

(2, 3, 6, 3, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 3  1 1 0

(2, 3, 6, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 3  1 2 0

(2, 3, 6, 3, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 3  1 3 0

(2, 3, 6, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  1 1 0

(2, 3, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  2 3  2 2  −p^{3}(p − 1)

(2, 3, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 3  2 2  0

(2, 3, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  1 2  0

h(2, 3, 6, 4, 2) = p^{3} − p^{4}

(2, 3, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 3  2 3  0

(2, 3, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  1 3  0

h(2, 3, 6, 4, 3) = p^{3} − p^{4}

(2, 3, 6, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  1 4 0

(2, 3, 6, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  1 1 0

(2, 3, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  2 4  2 2  −p^{3}(p − 1)

(2, 3, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  2 2  0

(2, 3, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  1 2  0

h(2, 3, 6, 5, 2) = p^{3} − p^{4}

\begin{matrix}(2, 3, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  2 4  2 3 & 0 \\ (2, 3, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  2 3 & 0 \\ (2, 3, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  1 3 & 0 \end{matrix}

(2, 3, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  2 4  2 4  p^{3}(p − 1)

(2, 3, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  2 4  0

(2, 3, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  1 4  0

h(2, 3, 6, 5, 4) = −p^{3} + p^{4}

(2, 3, 6, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  1 5 0

(2, 3, 6, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  2 2 0

(2, 3, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  3 3  0

(2, 3, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  2 3  0

h(2, 3, 6, 6, 3) = −p^{3} + p^{4}

(2, 3, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  0 4  3  2 4  3 4  p^{3}(p − 1)

(2, 3, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 4  3 4  0

(2, 3, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  2 4  0

h(2, 3, 6, 6, 4) = −p^{3} + p^{4}

(2, 3, 6, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  2 5 0

(2, 3, 6, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  3 3 0

(2, 3, 6, 7, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  3 4 0

(2, 3, 6, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  1  0 5  3  1 5  3 5 0

(2, 4, 2, 0, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 1  0 0  p

h(2, 4, 2, 0, 0) = p

(2, 4, 2, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 1  0 1  p

h(2, 4, 2, 0, 1) = p

(2, 4, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 2  0 0  −p(p − 1)

(2, 4, 2, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 2  0 0  0

h(2, 4, 2, 1, 0) = p − p^{2}

\begin{matrix}(2, 4, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 2  0 1 & 0 \\ (2, 4, 2, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 2  0 1 & 0 \end{matrix}

(2, 4, 2, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 2  0 2  0

h(2, 4, 2, 1, 2) = −p + p^{2}

(2, 4, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  0 0 −p(p − 1)

(2, 4, 2, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 3  0 0  p(p − 1)

cancel

(2, 4, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 2  1 1  0

(2, 4, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  0 1  0

(2, 4, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 2  1 1  p(p − 1)

(2, 4, 2, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 3  0 1  0

h(2, 4, 2, 2, 1) = −p + p^{2}

(2, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  0 2  −p(p − 1)^{2}

(2, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 2  1 2  p(p − 1)

(2, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 3  0 2  p(p − 1)^{2}

h(2, 4, 2, 2, 2) = −p + p^{2}

(2, 4, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  0 3 −p^{2}(p − 1)

(2, 4, 2, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 3  0 3  p^{2}(p − 1)

cancel

(2, 4, 2, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 4  0 0  p^{2}

h(2, 4, 2, 3, 0) = p^{2}

\begin{matrix}(2, 4, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  1 1 & 0 \\ (2, 4, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 3  1 1 & 0 \\ (2, 4, 2, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 4  0 1 & 0 \end{matrix}

(2, 4, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  1 2  0

(2, 4, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 3  1 2  0

(2, 4, 2, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 4  0 2  p^{2}(p − 1)

h(2, 4, 2, 3, 2) = −p^{2} + p^{3}

\begin{matrix}(2, 4, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  1 3 & 0 \\ (2, 4, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 3  1 3 & 0 \\ (2, 4, 2, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 4  0 3 & 0 \end{matrix}

h(2, 4, 2, 3, 4) = −p^{3}

(2, 4, 2, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 4  1 1  −p^{2}

h(2, 4, 2, 4, 1) = −p^{2}

(2, 4, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  2 2  p^{2}(p − 1)

(2, 4, 2, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 4  1 2  0

h(2, 4, 2, 4, 2) = −p^{2} + p^{3}

(2, 4, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  0 3  2 3  p^{2}(p − 1)

(2, 4, 2, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 4  1 3 −p^{2}(p − 1)

cancel

(2, 4, 2, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  1  0 4  1 4  −p^{3}

h(2, 4, 2, 4, 4) = −p^{3}

h(2, 4, 3, 0, 0) = p

(2, 4, 3, 0, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 1  0 1  p

h(2, 4, 3, 0, 1) = p

\begin{matrix}(2, 4, 3, 1, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 2  0 0 & 0 \\ (2, 4, 3, 1, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 2  0 0 & 0 \\ (2, 4, 3, 1, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(2, 4, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 2  0 1 & 0 \\ (2, 4, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 2  0 1 & 0 \\ (2, 4, 3, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(2, 4, 3, 1, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 2  0 2 & 0 \\ (2, 4, 3, 1, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 2  0 2 & 0 \\ (2, 4, 3, 1, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 2  0 2 & 0 \end{matrix} (2, 4, 3, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  0 0  0 ; (2, 4, 3, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  0 0  0 ; (2, 4, 3, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 3  0 0  p(p − 1) ; h(2, 4, 3, 2, 0) = −p + p^{2}

357

(2, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  1 2  1 1  0

(2, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 2  1 1  0

(2, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  0 1  0

(2, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 2  1 1  0

(2, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  0 1  0

(2, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 2  1 1  p(p − 1)

(2, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 3  0 1  0

h(2, 4, 3, 2, 1) = −p + p^{2}

(2, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  1 2  1 2  0

(2, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 2  1 2  0

(2, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  0 2  0

(2, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 2  1 2  0

(2, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  0 2  0

(2, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 2  1 2  p(p − 1)

(2, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 3  0 2  p(p − 1)^{2}

h(2, 4, 3, 2, 2) = −p^{2} + p^{3}

(2, 4, 3, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  0 3  0 ; (2, 4, 3, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  0 3  0 ; (2, 4, 3, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 3  0 3  p^{2}(p − 1) ; h(2, 4, 3, 2, 3) = −p^{2} + p^{3} \begin{matrix}(2, 4, 3, 3, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  0 0 & 0 \\ (2, 4, 3, 3, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  0 0 & 0 \\ (2, 4, 3, 3, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  0 0 & 0 \end{matrix}

360

\begin{matrix}(2, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 3  2  1 3  1 1 & 0 \\ (2, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  1 3  1 1 & 0 \\ (2, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  1 1 & 0 \\ (2, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  0 1 & 0 \\ (2, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  1 1 & 0 \\ (2, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  0 1 & 0 \\ (2, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 3  1 1 & 0 \\ (2, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  0 1 & 0 \end{matrix}

361

\begin{matrix}(2, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 3  2  1 3  1 2 & 0 \\ (2, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  1 3  1 2 & 0 \\ (2, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  1 2 & 0 \\ (2, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  0 2 & 0 \\ (2, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  1 2 & 0 \\ (2, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  0 2 & 0 \\ (2, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 3  1 2 & 0 \\ (2, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  0 2 & 0 \end{matrix}

362

\begin{matrix}(2, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 3  2  1 3  1 3 & 0 \\ (2, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  1 3  1 3 & 0 \\ (2, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  1 3 & 0 \\ (2, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  0 3 & 0 \\ (2, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  1 3 & 0 \\ (2, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  0 3 & 0 \\ (2, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 3  1 3 & 0 \\ (2, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  0 3 & 0 \end{matrix}

363

\begin{matrix}(2, 4, 3, 3, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  0 4 & 0 \\ (2, 4, 3, 3, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  0 4 & 0 \\ (2, 4, 3, 3, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  0 4 & 0 \end{matrix}

(2, 4, 3, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  0 0  −p^{2}

h(2, 4, 3, 4, 0) = −p^{2}

(2, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  1 1  0

(2, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  1 1  0

(2, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  1 1  p^{2}(p − 1)

(2, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  0 1  0

h(2, 4, 3, 4, 1) = −p^{2} + p^{3}

(2, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  1 3  2 2  0

(2, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  2 2  0

(2, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  1 2  0

(2, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  2 2  0

(2, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  1 2  0

(2, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  1 2  0

(2, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  0 2  −p^{2}(p − 1)

h(2, 4, 3, 4, 2) = p^{2} − p^{3}

(2, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 3  2  1 3  2 3  0

(2, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 3  2 3  0

(2, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  1 3  0

(2, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 3  2 3  0

(2, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  1 3  0

(2, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  1 3  p^{2}(p − 1)^{2}

(2, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  0 3  0

h(2, 4, 3, 4, 3) = p^{2} − 2p^{3} + p^{4}

(2, 4, 3, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  1 4  0

(2, 4, 3, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 4  1 4  p^{3}(p − 1)

(2, 4, 3, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  0 4 −p^{3}(p − 1)

cancel

(2, 4, 3, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  0 5  −p^{4}

h(2, 4, 3, 4, 5) = −p^{4}

(2, 4, 3, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  1 1  p^{3}

h(2, 4, 3, 5, 1) = p^{3}

\begin{matrix}(2, 4, 3, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  2 2 & 0 \\ (2, 4, 3, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  2 2 & 0 \\ (2, 4, 3, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  1 2 & 0 \end{matrix}

(2, 4, 3, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  2 3  0

(2, 4, 3, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  2 3  0

(2, 4, 3, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  1 3  p^{3}(p − 1)

h(2, 4, 3, 5, 3) = −p^{3} + p^{4}

\begin{matrix}(2, 4, 3, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  0 4  2 4 & 0 \\ (2, 4, 3, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  0 4  2 4 & 0 \\ (2, 4, 3, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  1  0 5  1 4 & 0 \end{matrix}

h(2, 4, 3, 5, 5) = −p^{4}

(2, 4, 4, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 2  0 0  p(p − 1)

(2, 4, 4, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 2  0 0  0

h(2, 4, 4, 1, 0) = −p + p^{2}

\begin{matrix}(2, 4, 4, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 2  0 1 & 0 \\ (2, 4, 4, 1, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 2  0 1 & 0 \end{matrix}

(2, 4, 4, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 2  0 2  −p(p − 1)

(2, 4, 4, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 2  0 2  0

h(2, 4, 4, 1, 2) = p − p^{2}

(2, 4, 4, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  0 0  0

(2, 4, 4, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  0 0  p^{2}(p − 1)

(2, 4, 4, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 3  0 0  0

h(2, 4, 4, 2, 0) = −p + p^{2}

(2, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 2  1 1  0

(2, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 3  0 1  0

(2, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 2  1 1  0

(2, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  0 1  0

(2, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 2  1 1  p^{2}(p − 1)

(2, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  0 1  0

(2, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 2  1 1  0

(2, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 3  0 1  0

h(2, 4, 4, 2, 1) = −p^{2} + p^{3}

(2, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 2  1 2  0

(2, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 3  0 2  −p(p − 1)^{3}

(2, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 2  1 2  0

(2, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  0 2  0

(2, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 2  1 2  p^{2}(p − 1)

(2, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  0 2  p^{2}(p − 1)^{2}

(2, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 2  1 2  0

(2, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 3  0 2  0

h(2, 4, 4, 2, 2) = p − 3p^{2} + 2p^{3}

(2, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 3  0 3  −p^{2}(p − 1)^{2} ; (2, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  0 3  0 ; (2, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  0 3  p^{3}(p − 1) ; (2, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 3  0 3  0 ; h(2, 4, 4, 2, 3) = −p^{2} + p^{3} (2, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  0 0  −p(p − 1)^{2} ; (2, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  0 0  p(p − 1)^{2} ; (2, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  0 0  p^{2}(p − 1) ; (2, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  0 0  0 ; h(2, 4, 4, 3, 0) = −p^{2} + p^{3}

373

\begin{matrix}(2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 3  1 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 3  1 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 3  1 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  0 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  1 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  0 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 3  1 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  1 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  0 1 & 0 \end{matrix}

374

\begin{matrix}(2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 3  1 1 & 0 \\ (2, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  0 1 & 0 \end{matrix}

375

\begin{matrix}(2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 3  1 2 & 0 \\ (2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 3  1 2 & 0 \\ (2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 3  1 2 & 0 \\ (2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  0 2 & −p(p − 1)^{3} \\ (2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  1 2 & 0 \\ (2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  0 2 & p(p − 1)^{3} \\ (2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 3  1 2 & 0 \\ (2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  1 2 & 0 \\ (2, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  0 2 & p^{2}(p − 1)^{2} \end{matrix}

376

(2, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  0 2  0

h(2, 4, 4, 3, 2) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 3  1 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 3  1 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 3  1 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  0 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  1 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  0 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 3  1 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  1 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  0 3 & 0 \end{matrix}

378

\begin{matrix}(2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 3  1 3 & 0 \\ (2, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  0 3 & 0 \end{matrix}

(2, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  0 4  p^{2}(p − 1)^{2}

(2, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  0 4  −p^{2}(p − 1)^{2}

(2, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  0 4  −p^{3}(p − 1)

(2, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  0 4  0

h(2, 4, 4, 3, 4) = p^{3} − p^{4}

(2, 4, 4, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  0 0  p^{2}(p − 1)

(2, 4, 4, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  0 0  0

h(2, 4, 4, 4, 0) = −p^{2} + p^{3}

(2, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 4  1 1  0

(2, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  1 1  0

(2, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  1 1  0

(2, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  0 1  0

(2, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 4  1 1  −p^{2}(p − 1)

(2, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  1 1  0

(2, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  1 1  0

(2, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  0 1  0

h(2, 4, 4, 4, 1) = p^{2} − p^{3}

\begin{matrix}(2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 3  2 2 & 0 \\ (2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 4  1 2 & 0 \\ (2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 3  2 2 & 0 \\ (2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 4  1 2 & 0 \\ (2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 3  2 2 & −p^{2}(p − 1)^{3} \\ (2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  1 2 & 0 \\ (2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  2 2 & 0 \\ (2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  1 2 & 0 \\ (2, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  0 2 & p^{2}(p − 1)^{2} \end{matrix}

381

(2, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 3  2 2  p^{2}(p − 1)^{2}

(2, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 4  1 2  0

(2, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  2 2  p^{3}(p − 1)^{2}

(2, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  1 2  0

(2, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 3  2 2  0

(2, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  1 2  0

(2, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  0 2  0

h(2, 4, 4, 4, 2) = 3p^{2} − 6p^{3} + 3p^{4}

\begin{matrix}(2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 3  2 3 & 0 \\ (2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 4  1 3 & 0 \\ (2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 3  2 3 & 0 \\ (2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 4  1 3 & 0 \\ (2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 3  2 3 & −p^{2}(p − 1)^{3} \\ (2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  1 3 & 0 \\ (2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 3  2 3 & 0 \\ (2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  1 3 & 0 \\ (2, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  0 3 & 0 \end{matrix}

383

(2, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 4  1 3  −p^{2}(p − 1)^{2}

(2, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 3  2 3  p^{3}(p − 1)^{2}

(2, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  1 3  0

(2, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 3  2 3  0

(2, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  1 3  0

(2, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  0 3  0

h(2, 4, 4, 4, 3) = p^{2} − 2p^{3} + p^{4}

(2, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 4  1 4  0

(2, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  1 4  0

(2, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  1 4  0

(2, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  0 4  p^{3}(p − 1)^{2}

(2, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 4  1 4  −p^{3}(p − 1)

(2, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  1 4  0

(2, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  1 4  0

(2, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  0 4  0

h(2, 4, 4, 4, 4) = 2p^{3} − 3p^{4} + p^{5}

(2, 4, 4, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  0 5  p^{4}(p − 1) ; (2, 4, 4, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  0 5  0 ; h(2, 4, 4, 4, 5) = −p^{4} + p^{5} \begin{matrix}(2, 4, 4, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  1 1 & 0 \\ (2, 4, 4, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  1 1 & 0 \end{matrix}

386

\begin{matrix}(2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 4  2 2 & 0 \\ (2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 4  2 2 & 0 \\ (2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  2 2 & −p^{2}(p − 1)^{3} \\ (2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  2 2 & −p^{2}(p − 1)^{2} \\ (2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  1 2 & 0 \\ (2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 4  2 2 & p^{3}(p − 1) \\ (2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  2 2 & p^{3}(p − 1)^{2} \\ (2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  2 2 & 0 \\ (2, 4, 4, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  1 2 & 0 \end{matrix}

387

\begin{matrix}(2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  2  1 4  2 3 & 0 \\ (2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 4  2 3 & 0 \\ (2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  2 3 & 0 \\ (2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  2 3 & 0 \\ (2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  1 3 & 0 \\ (2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 4  2 3 & 0 \\ (2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  2 3 & 0 \\ (2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  2 3 & 0 \\ (2, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  1 3 & 0 \end{matrix}

388

(2, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  2  1 4  2 4  0

(2, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  2 4  p^{2}(p − 1)^{3}

(2, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 4  2 4  p^{2}(p − 1)^{2}

(2, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  1 4  0

(2, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  2  1 4  2 4  −p^{3}(p − 1)

(2, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  2 4  −p^{3}(p − 1)^{2}

(2, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 4  2 4  0

(2, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  1 4  0

h(2, 4, 4, 5, 4) = p^{3} − p^{4}

\begin{matrix}(2, 4, 4, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  1 5 & 0 \\ (2, 4, 4, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  1 5 & 0 \end{matrix}

(2, 4, 4, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  2 2  −p^{3}(p − 1)

(2, 4, 4, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  2 2  0

h(2, 4, 4, 6, 2) = p^{3} − p^{4}

(2, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  3 3  p^{3}(p − 1)^{2}

(2, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  2 3  0

(2, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  3 3  −p^{4}(p − 1)

(2, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  2 3  0

h(2, 4, 4, 6, 3) = p^{3} − p^{4}

(2, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  0 4  3 4  p^{3}(p − 1)^{2}
(2, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  2 4  −p^{3}(p − 1)^{2}
(2, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  0 4  3 4  −p^{4}(p − 1)
(2, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  2 4  0

h(2, 4, 4, 6, 4) = p^{4} − p^{5}

(2, 4, 4, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  0 5  2 5  −p^{4}(p − 1)
(2, 4, 4, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  0 5  2 5  0

h(2, 4, 4, 6, 5) = p^{4} − p^{5}

(2, 4, 5, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  0 0 −p^{2}(p − 1)
(2, 4, 5, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  0 0  p^{2}(p − 1)

cancel

(2, 4, 5, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 2  1 1  0 ; (2, 4, 5, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  0 1  0 ; (2, 4, 5, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 2  1 1  p^{2}(p − 1) ; (2, 4, 5, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  0 1  0 ; h(2, 4, 5, 2, 1) = −p^{2} + p^{3} (2, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 2  1 2  0 ; (2, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  0 2  −p^{2}(p − 1)^{2} ; (2, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 2  1 2  p^{2}(p − 1) ; (2, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  0 2  p^{2}(p − 1)^{2} ; h(2, 4, 5, 2, 2) = −p^{2} + p^{3}

392

(2, 4, 5, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  0 3 −p^{3}(p − 1) ; (2, 4, 5, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  0 3  p^{3}(p − 1) ; cancel \begin{matrix}(2, 4, 5, 3, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  0 0 & 0 \\ (2, 4, 5, 3, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  0 0 & 0 \end{matrix}

393

\begin{matrix}(2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 3  1 1 & 0 \\ (2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 3  1 1 & 0 \\ (2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 3  1 1 & 0 \\ (2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  1 1 & 0 \\ (2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  0 1 & 0 \\ (2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 3  1 1 & 0 \\ (2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 3  1 1 & 0 \\ (2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  1 1 & 0 \\ (2, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  0 1 & 0 \end{matrix}

394

\begin{matrix}(2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 3  1 2 & 0 \\ (2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 3  1 2 & 0 \\ (2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 3  1 2 & 0 \\ (2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  1 2 & 0 \\ (2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  0 2 & 0 \\ (2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 3  1 2 & 0 \\ (2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 3  1 2 & 0 \\ (2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  1 2 & 0 \\ (2, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  0 2 & 0 \end{matrix}

395

\begin{matrix}(2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 3  1 3 & 0 \\ (2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 3  1 3 & 0 \\ (2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 3  1 3 & 0 \\ (2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  1 3 & 0 \\ (2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  0 3 & 0 \\ (2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 3  1 3 & 0 \\ (2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 3  1 3 & 0 \\ (2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  1 3 & 0 \\ (2, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  0 3 & 0 \end{matrix}

396

\begin{matrix}(2, 4, 5, 3, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  0 4 & 0 \\ (2, 4, 5, 3, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  0 4 & 0 \end{matrix} (2, 4, 5, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  0 0  p^{2}(p − 1) ; (2, 4, 5, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  0 0 −p^{2}(p − 1) ; cancel

397

(2, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  1 1  0

(2, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 4  1 1  0

(2, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  1 1  0

(2, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  0 1  0

(2, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  1 1  0

(2, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 4  1 1  p^{2}(p − 1)^{2}

(2, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  1 1  0

(2, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  0 1  0

h(2, 4, 5, 4, 1) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 3  2 2 & 0 \\ (2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 4  1 2 & 0 \\ (2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 3  2 2 & 0 \\ (2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  1 2 & 0 \\ (2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 3  2 2 & 0 \\ (2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 4  1 2 & 0 \\ (2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  2 2 & −p^{3}(p − 1)^{2} \\ (2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  1 2 & 0 \\ (2, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  0 2 & p^{2}(p − 1)^{2} \end{matrix}

399

(2, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  1 2  0

(2, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 3  2 2  p^{2}(p − 1)^{2}

(2, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 4  1 2  0

(2, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  2 2  p^{3}(p − 1)^{2}

(2, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  1 2  0

(2, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  0 2  −p^{2}(p − 1)^{2}

h(2, 4, 5, 4, 2) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 3  2 3 & 0 \\ (2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 4  1 3 & 0 \\ (2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 3  2 3 & 0 \\ (2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  1 3 & 0 \\ (2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 3  2 3 & 0 \\ (2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 4  1 3 & 0 \\ (2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 3  2 3 & −p^{3}(p − 1)^{2} \\ (2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  1 3 & 0 \\ (2, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  0 3 & 0 \end{matrix}

401

(2, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  1 3  0

(2, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 3  2 3  p^{2}(p − 1)^{2}

(2, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 4  1 3  p^{2}(p − 1)^{3}

(2, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 3  2 3  p^{3}(p − 1)^{2}

(2, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  1 3  0

(2, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  0 3  0

h(2, 4, 5, 4, 3) = p^{3} − 2p^{4} + p^{5}

(2, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  1 4  0

(2, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 4  1 4  0

(2, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  1 4  0

(2, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  0 4  p^{3}(p − 1)^{2}

(2, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  1 4  0

(2, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 4  1 4  p^{3}(p − 1)^{2}

(2, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  1 4  0

(2, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  0 4  −p^{3}(p − 1)^{2}

h(2, 4, 5, 4, 4) = p^{3} − 2p^{4} + p^{5}

(2, 4, 5, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  0 5  p^{4}(p − 1) ; (2, 4, 5, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  0 5 −p^{4}(p − 1) ; cancel (2, 4, 5, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 5  1 1  0 ; (2, 4, 5, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  1 1  0 ; (2, 4, 5, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  1 1  p^{3}(p − 1) ; (2, 4, 5, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  1 1  0 ; h(2, 4, 5, 5, 1) = −p^{3} + p^{4}

404

\begin{matrix}(2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 4  2 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  2 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 4  2 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 5  1 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  2 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  1 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  2 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 4  2 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  1 2 & 0 \end{matrix}

405

\begin{matrix}(2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  2 2 & 0 \\ (2, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  1 2 & 0 \end{matrix}

406

\begin{matrix}(2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 4  2 3 & 0 \\ (2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  2 3 & 0 \\ (2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 4  2 3 & 0 \\ (2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 5  1 3 & 0 \\ (2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  2 3 & 0 \\ (2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  1 3 & 0 \\ (2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  2 3 & 0 \\ (2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 4  2 3 & 0 \\ (2, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  1 3 & p^{3}(p − 1)^{2} \end{matrix}

407

(2, 4, 5, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  1 3  0

h(2, 4, 5, 5, 3) = p^{3} − 2p^{4} + p^{5}

\begin{matrix}(2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 4  2 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  2 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 4  2 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 5  1 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  2 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  1 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  2 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 4  2 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  1 4 & 0 \end{matrix}

409

\begin{matrix}(2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  2 4 & 0 \\ (2, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  1 4 & 0 \end{matrix} (2, 4, 5, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 5  1 5  0 ; (2, 4, 5, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  1 5  0 ; (2, 4, 5, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  1 5  −p^{4}(p − 1) ; (2, 4, 5, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  1 5  0 ; h(2, 4, 5, 5, 5) = p^{4} − p^{5}

410

(2, 4, 5, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  2 2  p^{3}(p − 1)^{2}

(2, 4, 5, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  2 2  −p^{3}(p − 1)

(2, 4, 5, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  2 2  −p^{3}(p − 1)^{2}

h(2, 4, 5, 6, 2) = p^{3} − p^{4}

(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  1 4  3 3  0
(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  3 3  0
(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 5  2 3  0
(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  3 3 −p^{4}(p − 1)^{2}
(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  2 3  0
(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  3 3  0
(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  2 3  0
(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  3 3  p^{4}(p − 1)^{2}
(2, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  2 3  0

cancel

(2, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  1 4  3 4  0

(2, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  2  1 5  2 4  0

(2, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 4  3 4  −p^{4}(p − 1)^{2}

(2, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  2 4  p^{3}(p − 1)^{3}

(2, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 4  3  1 4  3 4  0

(2, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  2 4  −p^{3}(p − 1)^{2}

(2, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 4  3 4  p^{4}(p − 1)^{2}

(2, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  2 4  −p^{3}(p − 1)^{3}

h(2, 4, 5, 6, 4) = −p^{3} + 2p^{4} − p^{5}

(2, 4, 5, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  2 5  p^{4}(p − 1)^{2}

(2, 4, 5, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  2  1 5  2 5  −p^{4}(p − 1)

(2, 4, 5, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  2 5  −p^{4}(p − 1)^{2}

h(2, 4, 5, 6, 5) = p^{4} − p^{5}

(2, 4, 5, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  3 3 −p^{5}(p − 1)

(2, 4, 5, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  3 3  p^{5}(p − 1)

cancel

\begin{matrix}(2, 4, 5, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  0 5  3 4 & 0 \\ (2, 4, 5, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  3 4 & 0 \end{matrix}

(2, 4, 5, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  0 5  3 5 −p^{5}(p − 1)

cancel

(2, 4, 6, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  0 0  −p^{3}

h(2, 4, 6, 3, 0) = −p^{3}

\begin{matrix}(2, 4, 6, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 3  1 1 & 0 \\ (2, 4, 6, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 3  1 1 & 0 \\ (2, 4, 6, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  0 1 & 0 \end{matrix}

(2, 4, 6, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 3  1 2  0

(2, 4, 6, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  0 2  −p^{3}(p − 1)

h(2, 4, 6, 3, 2) = p^{3} − p^{4}

\begin{matrix}(2, 4, 6, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 3  1 3 & 0 \\ (2, 4, 6, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 3  1 3 & 0 \\ (2, 4, 6, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  0 3 & 0 \end{matrix}

(2, 4, 6, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  0 4  p^{4}

h(2, 4, 6, 3, 4) = p^{4}

(2, 4, 6, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  0 0  −p^{3}

h(2, 4, 6, 4, 0) = −p^{3}

\begin{matrix}(2, 4, 6, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 4  1 1 & 0 \\ (2, 4, 6, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  1 1 & 0 \\ (2, 4, 6, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  1 1 & 0 \\ (2, 4, 6, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  0 1 & 0 \end{matrix}

417

(2, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  2 3  2 2  p^{3}(p − 1)^{2}

(2, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 3  2 2  0

(2, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 4  1 2  0

(2, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 3  2 2  0

(2, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  1 2  0

(2, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  1 2  0

(2, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  0 2  −p^{3}(p − 1)

h(2, 4, 6, 4, 2) = 2p^{3} − 3p^{4} + p^{5}

(2, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  2 3  2 3  p^{3}(p − 1)^{2}

(2, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 3  2 3  0

(2, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 4  1 3  0

(2, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 3  2 3  0

(2, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  1 3  0

(2, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  1 3  0

(2, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  0 3  0

h(2, 4, 6, 4, 3) = p^{3} − 2p^{4} + p^{5}

(2, 4, 6, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  1 4  0

(2, 4, 6, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  1 4  0

(2, 4, 6, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  0 4  −p^{4}(p − 1)

h(2, 4, 6, 4, 4) = p^{4} − p^{5}

(2, 4, 6, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  0 5  −p^{5}

h(2, 4, 6, 4, 5) = −p^{5}

\begin{matrix}(2, 4, 6, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  1 1 & 0 \\ (2, 4, 6, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  1 1 & 0 \\ (2, 4, 6, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  1 1 & 0 \end{matrix}

(2, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  2 4  2 2  p^{3}(p − 1)^{2}

(2, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 4  2 2  0

(2, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  1 2  0

(2, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  2 2  0

(2, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  1 2  0

(2, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  2 2  −p^{4}(p − 1)

(2, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  1 2  0

h(2, 4, 6, 5, 2) = p^{3} − p^{4}

\begin{matrix}(2, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 4  3  2  1 4  3  2 4  2 3 & 0 \\ (2, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  2 4  2 3 & 0 \\ (2, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 4  2 3 & 0 \\ (2, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  1 3 & 0 \\ (2, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  2 3 & 0 \\ (2, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  1 3 & 0 \\ (2, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  2 3 & 0 \\ (2, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  1 3 & 0 \end{matrix}

422

(2, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  2 4  2 4  −p^{3}(p − 1)^{2}

(2, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 4  2 4  0

(2, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  1 4  0

(2, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  2 4  0

(2, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  1 4  0

(2, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  2 4  p^{4}(p − 1)

(2, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  1 4  0

h(2, 4, 6, 5, 4) = −p^{3} + p^{4}

\begin{matrix}(2, 4, 6, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  1 5 & 0 \\ (2, 4, 6, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  1 5 & 0 \\ (2, 4, 6, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  1 5 & 0 \end{matrix} (2, 4, 6, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  2 2  0 ; (2, 4, 6, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  2 2  0 ; (2, 4, 6, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  2 2  −p^{4}(p − 1) ; h(2, 4, 6, 6, 2) = p^{4} − p^{5}

424

(2, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  2 4  3 3  −p^{3}(p − 1)^{2}

(2, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 4  3 3  0

(2, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  2 3  0

(2, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  3 3  0

(2, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  2 3  0

(2, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  3 3  0

(2, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  2 3  0

h(2, 4, 6, 6, 3) = −p^{3} + 2p^{4} − p^{5}

(2, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 4  3  2 4  3 4  −p^{3}(p − 1)^{2}

(2, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 4  3 4  0

(2, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  2 4  0

(2, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 4  3 4  0

(2, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  2 4  0

(2, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 4  3 4  0

(2, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  2 4  −p^{4}(p − 1)^{2}

h(2, 4, 6, 6, 4) = −p^{3} + p^{4} + p^{5} − p^{6}

(2, 4, 6, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  2 5  0

(2, 4, 6, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  2 5  −p^{5}(p − 1)

h(2, 4, 6, 6, 5) = p^{5} − p^{6}

\begin{matrix}(2, 4, 6, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  3 3 & 0 \\ (2, 4, 6, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  3 3 & 0 \\ (2, 4, 6, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  3 3 & 0 \end{matrix}

\begin{matrix}(2, 4, 6, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  3 4 & 0 \\ (2, 4, 6, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  3 4 & 0 \\ (2, 4, 6, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  3 4 & 0 \end{matrix}

\begin{matrix}(2, 4, 6, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  1 5  3 5 & 0 \\ (2, 4, 6, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  3  1 5  3 5 & 0 \\ (2, 4, 6, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  3 5 & 0 \end{matrix}

(2, 4, 6, 8, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  4 4  p^{6}

h(2, 4, 6, 8, 4) = p^{6}

(2, 4, 6, 8, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  0 5  4 5  p^{6}

h(2, 4, 6, 8, 5) = p^{6}

(2, 4, 7, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  1 1  −p^{4}

h(2, 4, 7, 4, 1) = −p^{4}

(2, 4, 7, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 3  2 2  p^{4}(p − 1)

(2, 4, 7, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  1 2  0

h(2, 4, 7, 4, 2) = −p^{4} + p^{5}

(2, 4, 7, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  1 3 −p^{4}(p − 1)

cancel

(2, 4, 7, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  1 4  −p^{5}

h(2, 4, 7, 4, 4) = −p^{5}

(2, 4, 7, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  1 1  −p^{4}

h(2, 4, 7, 5, 1) = −p^{4}

\begin{matrix}(2, 4, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 4  2 2 & 0 \\ (2, 4, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  2 2 & 0 \\ (2, 4, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  1 2 & 0 \end{matrix}

(2, 4, 7, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  2 3  0

(2, 4, 7, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  1 3  −p^{4}(p − 1)

h(2, 4, 7, 5, 3) = p^{4} − p^{5}

\begin{matrix}(2, 4, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 4  2 4 & 0 \\ (2, 4, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  2 4 & 0 \\ (2, 4, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  1 4 & 0 \end{matrix}

(2, 4, 7, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  1 5  p^{5}

h(2, 4, 7, 5, 5) = p^{5}

(2, 4, 7, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 5  2 2  −p^{4}(p − 1) ; (2, 4, 7, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  2 2  0 ; h(2, 4, 7, 6, 2) = p^{4} − p^{5} (2, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 4  3 3  p^{4}(p − 1)^{2} ; (2, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 5  2 3  0 ; (2, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  3 3  −p^{5}(p − 1) ; (2, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  2 3  0 ; h(2, 4, 7, 6, 3) = p^{4} − p^{5}

431

(2, 4, 7, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 4  3 4  p^{4}(p − 1)^{2}
(2, 4, 7, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 5  2 4  −p^{4}(p − 1)^{2}
(2, 4, 7, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 4  3 4  −p^{5}(p − 1)
(2, 4, 7, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  2 4  0

h(2, 4, 7, 6, 4) = p^{5} − p^{6}

(2, 4, 7, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 5  2 5  −p^{5}(p − 1)
(2, 4, 7, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  2 5  0

h(2, 4, 7, 6, 5) = p^{5} − p^{6}

(2, 4, 7, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 5  3 3  p^{5}(p − 1)
(2, 4, 7, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  3 3 −p^{5}(p − 1)

cancel

\begin{matrix}(2, 4, 7, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 5  3 4 & 0 \\ (2, 4, 7, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  3 4 & 0 \end{matrix}

(2, 4, 7, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  0 5  3  2 5  3 5 −p^{5}(p − 1)

(2, 4, 7, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  3 5  p^{5}(p − 1)

cancel

(2, 4, 7, 8, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  4 4  p^{6}

h(2, 4, 7, 8, 4) = p^{6}

(2, 4, 7, 8, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  1  0 5  4  1 5  4 5  p^{6}

h(2, 4, 7, 8, 5) = p^{6}

(2, 5, 3, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 2  0 0  p^{2}

h(2, 5, 3, 1, 0) = p^{2}

(2, 5, 3, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 2  0 1 0

h(2, 5, 3, 1, 2) = −p^{2}

(2, 5, 3, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  0 0 0

\begin{matrix}(2, 5, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 3  2  1 2  1 1 & 0 \\ (2, 5, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 2  1 1 & 0 \\ (2, 5, 3, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(2, 5, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 3  2  1 2  1 2 & 0 \\ (2, 5, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 2  1 2 & 0 \\ (2, 5, 3, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  0 2 & 0 \end{matrix}

(2, 5, 3, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  0 3 0

h(2, 5, 3, 3, 0) = −p^{2}

\begin{matrix}(2, 5, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 3  2  1 3  1 1 & 0 \\ (2, 5, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  1 1 & 0 \\ (2, 5, 3, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  0 1 & 0 \end{matrix}

(2, 5, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 3  2  1 3  1 2  0

(2, 5, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  1 2  0

(2, 5, 3, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  0 2  −p^{2}(p − 1)

h(2, 5, 3, 3, 2) = p^{2} − p^{3}

\begin{matrix}(2, 5, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 3  2  1 3  1 3 & 0 \\ (2, 5, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  1 3 & 0 \\ (2, 5, 3, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  0 3 & 0 \end{matrix}

(2, 5, 3, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  0 4  p^{3}

h(2, 5, 3, 3, 4) = p^{3}

(2, 5, 3, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  1 1 0

\begin{matrix}(2, 5, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 3  2  1 3  2 2 & 0 \\ (2, 5, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  2 2 & 0 \\ (2, 5, 3, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(2, 5, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 3  2  1 3  2 3 & 0 \\ (2, 5, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 3  2 3 & 0 \\ (2, 5, 3, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  1 3 & 0 \end{matrix}

(2, 5, 3, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  1 4 0

(2, 5, 3, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  2 2  p^{3}

h(2, 5, 3, 5, 2) = p^{3}

(2, 5, 3, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  2 3 0

(2, 5, 3, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  0 4  2 4  −p^{3}

h(2, 5, 3, 5, 4) = −p^{3}

(2, 5, 4, 1, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 2  0 0  p^{2}

h(2, 5, 4, 1, 0) = p^{2}

(2, 5, 4, 1, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 2  0 1 0

(2, 5, 4, 1, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 2  0 2  −p^{2}

h(2, 5, 4, 1, 2) = −p^{2}

\begin{matrix}(2, 5, 4, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  0 0 & 0 \\ (2, 5, 4, 2, 0) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  0 0 & 0 \end{matrix}

\begin{matrix}(2, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 2  1 1 & 0 \\ (2, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 2  1 1 & 0 \\ (2, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  0 1 & 0 \\ (2, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 2  1 1 & 0 \\ (2, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(2, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 2  1 2 & 0 \\ (2, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 2  1 2 & 0 \\ (2, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  0 2 & 0 \\ (2, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 2  1 2 & 0 \\ (2, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  0 2 & 0 \end{matrix}

\begin{matrix}(2, 5, 4, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  0 3 & 0 \\ (2, 5, 4, 2, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  0 3 & 0 \end{matrix}

(2, 5, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  0 0  0

(2, 5, 4, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  0 0  p^{2}(p − 1)

h(2, 5, 4, 3, 0) = −p^{2} + p^{3}

\begin{matrix}(2, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 3  1 1 & 0 \\ (2, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 3  1 1 & 0 \\ (2, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  1 1 & 0 \\ (2, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  0 1 & 0 \\ (2, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  1 1 & 0 \\ (2, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  0 1 & 0 \end{matrix}

440

(2, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 3  1 2  0

(2, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  1 2  0

(2, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  0 2  0

(2, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  1 2  0

(2, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  0 2  p^{2}(p − 1)^{2}

h(2, 5, 4, 3, 2) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(2, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 3  1 3 & 0 \\ (2, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 3  1 3 & 0 \\ (2, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  1 3 & 0 \\ (2, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  0 3 & 0 \\ (2, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  1 3 & 0 \\ (2, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  0 3 & 0 \end{matrix} (2, 5, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  0 4  0 ; (2, 5, 4, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  0 4  −p^{3}(p − 1) ; h(2, 5, 4, 3, 4) = p^{3} − p^{4}

442

(2, 5, 4, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  0 0  p^{3} ; h(2, 5, 4, 4, 0) = p^{3} \begin{matrix}(2, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 4  1 1 & 0 \\ (2, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 4  1 1 & 0 \\ (2, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  1 1 & 0 \\ (2, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  1 1 & 0 \\ (2, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  0 1 & 0 \end{matrix}

443

(2, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 4  1 2  0

(2, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 3  2 2  0

(2, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 4  1 2  0

(2, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  2 2  0

(2, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  1 2  0

(2, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  2 2  0

(2, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  1 2  0

(2, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  0 2  p^{3}(p − 1)

h(2, 5, 4, 4, 2) = −p^{3} + p^{4}

\begin{matrix}(2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 3  2 3 & 0 \\ (2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 4  1 3 & 0 \\ (2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 3  2 3 & 0 \\ (2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 4  1 3 & 0 \\ (2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 3  2 3 & 0 \\ (2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  1 3 & 0 \\ (2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 3  2 3 & 0 \\ (2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  1 3 & 0 \\ (2, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  0 3 & 0 \end{matrix}

445

(2, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 4  1 4  0

(2, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  1 4  0

(2, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  1 4  0

(2, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  0 4  p^{4}(p − 1)

h(2, 5, 4, 4, 4) = −p^{4} + p^{5}

(2, 5, 4, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  0 5  p^{5}

h(2, 5, 4, 4, 5) = p^{5}

(2, 5, 4, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  1 1 0

(2, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 4  2 2  0

(2, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  2 2  0

(2, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  2 2  −p^{3}(p − 1)

(2, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  1 2  0

h(2, 5, 4, 5, 2) = p^{3} − p^{4}

\begin{matrix}(2, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  2  1 4  2 3 & 0 \\ (2, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 4  2 3 & 0 \\ (2, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  2 3 & 0 \\ (2, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  2 3 & 0 \\ (2, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  1 3 & 0 \end{matrix}

448

(2, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  2  1 4  2 4  0

(2, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  2 4  0

(2, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 4  2 4  p^{3}(p − 1)

(2, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  1 4  0

h(2, 5, 4, 5, 4) = −p^{3} + p^{4}

(2, 5, 4, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  1 5 0

(2, 5, 4, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  2 2  −p^{4}

h(2, 5, 4, 6, 2) = −p^{4}

\begin{matrix}(2, 5, 4, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  3 3 & 0 \\ (2, 5, 4, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  2 3 & 0 \end{matrix}

(2, 5, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  0 4  3 4  0

(2, 5, 4, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  2 4  −p^{4}(p − 1)

h(2, 5, 4, 6, 4) = p^{4} − p^{5}

(2, 5, 4, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  0 5  2 5  −p^{5}

h(2, 5, 4, 6, 5) = −p^{5}

(2, 5, 5, 2, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  0 0 0

\begin{matrix}(2, 5, 5, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 2  1 1 & 0 \\ (2, 5, 5, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 2  1 1 & 0 \\ (2, 5, 5, 2, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(2, 5, 5, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 2  1 2 & 0 \\ (2, 5, 5, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 2  1 2 & 0 \\ (2, 5, 5, 2, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  0 2 & 0 \end{matrix}

(2, 5, 5, 2, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  0 3 0

(2, 5, 5, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  0 0 0

\begin{matrix}(2, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 3  1 1 & 0 \\ (2, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 3  1 1 & 0 \\ (2, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 3  1 1 & 0 \\ (2, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 3  1 1 & 0 \\ (2, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  1 1 & 0 \\ (2, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  0 1 & 0 \end{matrix}

452

\begin{matrix}(2, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 3  1 2 & 0 \\ (2, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 3  1 2 & 0 \\ (2, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 3  1 2 & 0 \\ (2, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 3  1 2 & 0 \\ (2, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  1 2 & 0 \\ (2, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  0 2 & 0 \end{matrix}

453

\begin{matrix}(2, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 3  1 3 & 0 \\ (2, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 3  1 3 & 0 \\ (2, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 3  1 3 & 0 \\ (2, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 3  1 3 & 0 \\ (2, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  1 3 & 0 \\ (2, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  0 3 & 0 \end{matrix}

(2, 5, 5, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  0 4 0

(2, 5, 5, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  0 0 0

\begin{matrix}(2, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  1 1 & 0 \\ (2, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 4  1 1 & 0 \\ (2, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  1 1 & 0 \\ (2, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 4  1 1 & 0 \\ (2, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  1 1 & 0 \\ (2, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  0 1 & 0 \end{matrix}

455

\begin{matrix}(2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 3  2 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  1 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 3  2 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 4  1 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 3  2 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  1 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 3  2 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 4  1 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  2 2 & 0 \end{matrix}

456

\begin{matrix}(2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  1 2 & 0 \\ (2, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  0 2 & 0 \end{matrix}

457

\begin{matrix}(2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 3  2 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  1 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 3  2 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 4  1 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 3  2 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  1 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 3  2 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 4  1 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 3  2 3 & 0 \end{matrix}

458

\begin{matrix}(2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  1 3 & 0 \\ (2, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  0 3 & 0 \end{matrix}

\begin{matrix}(2, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  1 4 & 0 \\ (2, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 4  1 4 & 0 \\ (2, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  1 4 & 0 \\ (2, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 4  1 4 & 0 \\ (2, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  1 4 & 0 \\ (2, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  0 4 & 0 \end{matrix}

(2, 5, 5, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  0 5 0

\begin{matrix}(2, 5, 5, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  1 1 & 0 \\ (2, 5, 5, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  1 1 & 0 \\ (2, 5, 5, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  1 1 & 0 \end{matrix}

460

\begin{matrix}(2, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  2 2 & 0 \\ (2, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 4  2 2 & 0 \\ (2, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  1 2 & 0 \\ (2, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  2 2 & 0 \\ (2, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 4  2 2 & 0 \\ (2, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  1 2 & 0 \\ (2, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  2 2 & 0 \\ (2, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  1 2 & 0 \end{matrix}

461

\begin{matrix}(2, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  2 3 & 0 \\ (2, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 4  2 3 & 0 \\ (2, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  1 3 & 0 \\ (2, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  2 3 & 0 \\ (2, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 4  2 3 & 0 \\ (2, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  1 3 & 0 \\ (2, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  2 3 & 0 \\ (2, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  1 3 & 0 \end{matrix}

462

\begin{matrix}(2, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  2 4 & 0 \\ (2, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 4  2 4 & 0 \\ (2, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  1 4 & 0 \\ (2, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  2 4 & 0 \\ (2, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 4  2 4 & 0 \\ (2, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  1 4 & 0 \\ (2, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  2 4 & 0 \\ (2, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  1 4 & 0 \end{matrix}

463

\begin{matrix}(2, 5, 5, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  1 5 & 0 \\ (2, 5, 5, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  1 5 & 0 \\ (2, 5, 5, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  1 5 & 0 \end{matrix} \begin{matrix}(2, 5, 5, 6, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  2 2 & 0 \\ (2, 5, 5, 6, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  2 2 & 0 \\ (2, 5, 5, 6, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  2 2 & 0 \end{matrix}

464

\begin{matrix}(2, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  3 3 & 0 \\ (2, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  2 3 & 0 \\ (2, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  3 3 & 0 \\ (2, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  2 3 & 0 \\ (2, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  3 3 & 0 \\ (2, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  2 3 & 0 \end{matrix}

465

\begin{matrix}(2, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  1 4  3 4 & 0 \\ (2, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  2 4 & 0 \\ (2, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  1 4  3 4 & 0 \\ (2, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  2 4 & 0 \\ (2, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 4  3 4 & 0 \\ (2, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  2 4 & 0 \end{matrix} \begin{matrix}(2, 5, 5, 6, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  2  1 5  2 5 & 0 \\ (2, 5, 5, 6, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  2  1 5  2 5 & 0 \\ (2, 5, 5, 6, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  2 5 & 0 \end{matrix}

466

(2, 5, 5, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  3 3 0

(2, 5, 5, 7, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  3 4 0

(2, 5, 5, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  0 5  3 5 0

(2, 5, 6, 3, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  0 0  −p^{3}

h(2, 5, 6, 3, 0) = −p^{3}

\begin{matrix}(2, 5, 6, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 3  1 1 & 0 \\ (2, 5, 6, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 3  1 1 & 0 \\ (2, 5, 6, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  0 1 & 0 \end{matrix}

(2, 5, 6, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 3  1 2  0

(2, 5, 6, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  0 2  −p^{3}(p − 1)

h(2, 5, 6, 3, 2) = p^{3} − p^{4}

\begin{matrix}(2, 5, 6, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 3  1 3 & 0 \\ (2, 5, 6, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 3  1 3 & 0 \\ (2, 5, 6, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  0 3 & 0 \end{matrix}

(2, 5, 6, 3, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  0 4  p^{4}

h(2, 5, 6, 3, 4) = p^{4}

(2, 5, 6, 4, 0) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  0 0  −p^{3}

h(2, 5, 6, 4, 0) = −p^{3}

\begin{matrix}(2, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 4  1 1 & 0 \\ (2, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  1 1 & 0 \\ (2, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  1 1 & 0 \\ (2, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  0 1 & 0 \end{matrix}

469

(2, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 3  2 2  0

(2, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 4  1 2  0

(2, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  2 3  2 2  0

(2, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 3  2 2  0

(2, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  1 2  0

(2, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  1 2  0

(2, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  0 2  −p^{3}(p − 1)

h(2, 5, 6, 4, 2) = p^{3} − p^{4}

\begin{matrix}(2, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  2 3  2 3 & 0 \\ (2, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 3  2 3 & 0 \\ (2, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 4  1 3 & 0 \\ (2, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  2 3  2 3 & 0 \\ (2, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 3  2 3 & 0 \\ (2, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  1 3 & 0 \\ (2, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  1 3 & 0 \\ (2, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  0 3 & 0 \end{matrix}

471

(2, 5, 6, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  1 4  0

(2, 5, 6, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  1 4  0

(2, 5, 6, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  0 4  −p^{4}(p − 1)

h(2, 5, 6, 4, 4) = p^{4} − p^{5}

(2, 5, 6, 4, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  0 5  −p^{5}

h(2, 5, 6, 4, 5) = −p^{5}

\begin{matrix}(2, 5, 6, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  1 1 & 0 \\ (2, 5, 6, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  1 1 & 0 \\ (2, 5, 6, 5, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  1 1 & 0 \end{matrix}

(2, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 4  2 2  0

(2, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  1 2  0

(2, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  2 4  2 2  0

(2, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  2 2  0

(2, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  1 2  0

(2, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  2 2  −p^{4}(p − 1)

(2, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  1 2  0

h(2, 5, 6, 5, 2) = p^{4} − p^{5}

\begin{matrix}(2, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  2 4  2 3 & 0 \\ (2, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 4  2 3 & 0 \\ (2, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  1 3 & 0 \\ (2, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  2 4  2 3 & 0 \\ (2, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  2 3 & 0 \\ (2, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  1 3 & 0 \\ (2, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  2 3 & 0 \\ (2, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  1 3 & 0 \end{matrix}

474

(2, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 4  2 4  0

(2, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  1 4  0

(2, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  2 4  2 4  0

(2, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  2 4  0

(2, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  1 4  0

(2, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  2 4  p^{4}(p − 1)

(2, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  1 4  0

h(2, 5, 6, 5, 4) = −p^{4} + p^{5}

\begin{matrix}(2, 5, 6, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  1 5 & 0 \\ (2, 5, 6, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  1 5 & 0 \\ (2, 5, 6, 5, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  1 5 & 0 \end{matrix} (2, 5, 6, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  2 2  0 ; (2, 5, 6, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  2 2  0 ; (2, 5, 6, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  2 2  −p^{4}(p − 1) ; h(2, 5, 6, 6, 2) = p^{4} − p^{5}

476

\begin{matrix}(2, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 4  3  2 4  3 3 & 0 \\ (2, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 4  3 3 & 0 \\ (2, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  2 3 & 0 \\ (2, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  2 4  3 3 & 0 \\ (2, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  3 3 & 0 \\ (2, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  2 3 & 0 \\ (2, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  3 3 & 0 \\ (2, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  2 3 & 0 \end{matrix}

477

(2, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 4  3 4  0

(2, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  2 4  0

(2, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 4  3  2 4  3 4  0

(2, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 4  3 4  0

(2, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  2 4  0

(2, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 4  3 4  0

(2, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  2 4  −p^{4}(p − 1)^{2}

h(2, 5, 6, 6, 4) = −p^{4} + 2p^{5} − p^{6}

(2, 5, 6, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  2 5  0

(2, 5, 6, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  2 5  −p^{5}(p − 1)

h(2, 5, 6, 6, 5) = p^{5} − p^{6}

\begin{matrix}(2, 5, 6, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  3 3 & 0 \\ (2, 5, 6, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  3 3 & 0 \\ (2, 5, 6, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  3 3 & 0 \end{matrix}

\begin{matrix}(2, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  3 4 & 0 \\ (2, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  3 4 & 0 \\ (2, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  3 4 & 0 \end{matrix}

\begin{matrix}(2, 5, 6, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  1 5  3 5 & 0 \\ (2, 5, 6, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  1 5  3 5 & 0 \\ (2, 5, 6, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  3 5 & 0 \end{matrix}

(2, 5, 6, 8, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  4 4  p^{6}

h(2, 5, 6, 8, 4) = p^{6}

(2, 5, 6, 8, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  0 5  4 5  p^{6}

h(2, 5, 6, 8, 5) = p^{6}

(2, 5, 7, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  1 1 0

\begin{matrix}(2, 5, 7, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 3  2 2 & 0 \\ (2, 5, 7, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 3  2 2 & 0 \\ (2, 5, 7, 4, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(2, 5, 7, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 3  2 3 & 0 \\ (2, 5, 7, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 3  2 3 & 0 \\ (2, 5, 7, 4, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  1 3 & 0 \end{matrix}

(2, 5, 7, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  1 4 0

(2, 5, 7, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  1 1 0

\begin{matrix}(2, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 4  2 2 & 0 \\ (2, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 4  2 2 & 0 \\ (2, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  2 2 & 0 \\ (2, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  1 2 & 0 \end{matrix} \begin{matrix}(2, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 4  2 3 & 0 \\ (2, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 4  2 3 & 0 \\ (2, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  2 3 & 0 \\ (2, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  1 3 & 0 \end{matrix}

482

\begin{matrix}(2, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 4  2 4 & 0 \\ (2, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 4  2 4 & 0 \\ (2, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  2 4 & 0 \\ (2, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  1 4 & 0 \end{matrix}

(2, 5, 7, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  1 5 0

\begin{matrix}(2, 5, 7, 6, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 5  2 2 & 0 \\ (2, 5, 7, 6, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 5  2 2 & 0 \\ (2, 5, 7, 6, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  2 2 & 0 \end{matrix}

\begin{matrix}(2, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 4  3 3 & 0 \\ (2, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 5  2 3 & 0 \\ (2, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 4  3 3 & 0 \\ (2, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 5  2 3 & 0 \\ (2, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  3 3 & 0 \\ (2, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  2 3 & 0 \end{matrix}

484

\begin{matrix}(2, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 4  3 4 & 0 \\ (2, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 5  2 4 & 0 \\ (2, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 4  3 4 & 0 \\ (2, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 5  2 4 & 0 \\ (2, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 4  3 4 & 0 \\ (2, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  2 4 & 0 \end{matrix} \begin{matrix}(2, 5, 7, 6, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 5  2 5 & 0 \\ (2, 5, 7, 6, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 5  2 5 & 0 \\ (2, 5, 7, 6, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  2 5 & 0 \end{matrix}

485

\begin{matrix}(2, 5, 7, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 5  3 3 & 0 \\ (2, 5, 7, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 5  3 3 & 0 \\ (2, 5, 7, 7, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  3 3 & 0 \end{matrix}

\begin{matrix}(2, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 5  3 4 & 0 \\ (2, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 5  3 4 & 0 \\ (2, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  3 4 & 0 \end{matrix}

\begin{matrix}(2, 5, 7, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  3  2  1 5  3  2 5  3 5 & 0 \\ (2, 5, 7, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  3  2 5  3 5 & 0 \\ (2, 5, 7, 7, 5) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  3 5 & 0 \end{matrix}

(2, 5, 7, 8, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  4 4 0

(2, 5, 7, 8, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  1 5  4 5 0

(2, 5, 8, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 4  2 2  p^{5}

h(2, 5, 8, 5, 2) = p^{5}

(2, 5, 8, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 4  2 3 0

(2, 5, 8, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 4  2 4  −p^{5}

h(2, 5, 8, 5, 4) = −p^{5}

(2, 5, 8, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  2 2  p^{5}

h(2, 5, 8, 6, 2) = p^{5}

\begin{matrix}(2, 5, 8, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 4  3 3 & 0 \\ (2, 5, 8, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  2 3 & 0 \end{matrix}

(2, 5, 8, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  2 4  p^{5}(p − 1)

h(2, 5, 8, 6, 4) = −p^{5} + p^{6}

(2, 5, 8, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  2 5  p^{6}

h(2, 5, 8, 6, 5) = p^{6}

(2, 5, 8, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  3 3 0

(2, 5, 8, 7, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  3 4 0

(2, 5, 8, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  3 5 0

(2, 5, 8, 8, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  4 4  −p^{6}

h(2, 5, 8, 8, 4) = −p^{6}

(2, 5, 8, 8, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  0 5  4  2 5  4 5  −p^{6}

h(2, 5, 8, 8, 5) = −p^{6}

h(2, 6, 4, 2, 1) = −p^{3}

(2, 6, 4, 2, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 2  1 2  −p^{3}

h(2, 6, 4, 2, 2) = −p^{3}

(2, 6, 4, 3, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 3  1 1 0

(2, 6, 4, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 3  1 2 0

(2, 6, 4, 3, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 3  1 3 0

(2, 6, 4, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 4  1 1  p^{3}

h(2, 6, 4, 4, 1) = p^{3}

(2, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 3  2 2  −p^{3}(p − 1)

(2, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 4  1 2  0

h(2, 6, 4, 4, 2) = p^{3} − p^{4}

(2, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 4  1 3  p^{3}(p − 1)

cancel

(2, 6, 4, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 4  1 4  p^{4}

h(2, 6, 4, 4, 4) = p^{4}

(2, 6, 4, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 4  2 2  −p^{4}

h(2, 6, 4, 5, 2) = −p^{4}

(2, 6, 4, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 4  2 3 0

(2, 6, 4, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  2  1 4  2 4  p^{4}

h(2, 6, 4, 5, 4) = p^{4}

(2, 6, 5, 2, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 2  1 1  −p^{3}

h(2, 6, 5, 2, 1) = −p^{3}

h(2, 6, 5, 2, 2) = −p^{3}

\begin{matrix}(2, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 3  1 1 & 0 \\ (2, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 3  1 1 & 0 \end{matrix}

\begin{matrix}(2, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 3  1 2 & 0 \\ (2, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 3  1 2 & 0 \end{matrix}

\begin{matrix}(2, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 3  1 3 & 0 \\ (2, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 3  1 3 & 0 \end{matrix}

(2, 6, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  1 1  0 ; (2, 6, 5, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 4  1 1  −p^{3}(p − 1) ; h(2, 6, 5, 4, 1) = p^{3} − p^{4} (2, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 3  2 2  0 ; (2, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  1 2  0 ; (2, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 3  2 2  −p^{3}(p − 1) ; (2, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 4  1 2  0 ; h(2, 6, 5, 4, 2) = p^{3} − p^{4}

492

(2, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  1 3  0

(2, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 3  2 3  −p^{3}(p − 1)

(2, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 4  1 3  −p^{3}(p − 1)^{2}

h(2, 6, 5, 4, 3) = p^{4} − p^{5}

(2, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  1 4  0

(2, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 4  1 4  −p^{4}(p − 1)

h(2, 6, 5, 4, 4) = p^{4} − p^{5}

(2, 6, 5, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 5  1 1  −p^{4}

h(2, 6, 5, 5, 1) = −p^{4}

\begin{matrix}(2, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  2 2 & 0 \\ (2, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 4  2 2 & 0 \\ (2, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 5  1 2 & 0 \end{matrix}

(2, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  2 3  0

(2, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 4  2 3  0

(2, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 5  1 3  −p^{4}(p − 1)

h(2, 6, 5, 5, 3) = p^{4} − p^{5}

\begin{matrix}(2, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  2 4 & 0 \\ (2, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 4  2 4 & 0 \\ (2, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 5  1 4 & 0 \end{matrix}

h(2, 6, 5, 5, 5) = p^{5}

(2, 6, 5, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 5  2 2  p^{4}

h(2, 6, 5, 6, 2) = p^{4}

\begin{matrix}(2, 6, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  3 3 & 0 \\ (2, 6, 5, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 5  2 3 & 0 \end{matrix}

(2, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  1 4  3 4  0

(2, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 5  2 4  p^{4}(p − 1)

h(2, 6, 5, 6, 4) = −p^{4} + p^{5}

(2, 6, 5, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  2  1 5  2 5  p^{5}

h(2, 6, 5, 6, 5) = p^{5}

(2, 6, 6, 3, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 3  1 1 0

(2, 6, 6, 3, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 3  1 2 0

(2, 6, 6, 3, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 3  1 3 0

(2, 6, 6, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  1 1 0

(2, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  2 3  2 2  −p^{4}(p − 1)

(2, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 3  2 2  0

(2, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  1 2  0

h(2, 6, 6, 4, 2) = p^{4} − p^{5}

(2, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 3  2 3  0

(2, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  1 3  0

h(2, 6, 6, 4, 3) = p^{4} − p^{5}

(2, 6, 6, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  1 4 0

(2, 6, 6, 5, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  1 1 0

(2, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  2 4  2 2  −p^{4}(p − 1)

(2, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  2 2  0

(2, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  1 2  0

h(2, 6, 6, 5, 2) = p^{4} − p^{5}

\begin{matrix}(2, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  2 4  2 3 & 0 \\ (2, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  2 3 & 0 \\ (2, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  1 3 & 0 \end{matrix}

(2, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  2 4  2 4  p^{4}(p − 1)

(2, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  2 4  0

(2, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  1 4  0

h(2, 6, 6, 5, 4) = −p^{4} + p^{5}

(2, 6, 6, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  1 5 0

(2, 6, 6, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  2 2 0

(2, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  3 3  0

(2, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  2 3  0

h(2, 6, 6, 6, 3) = −p^{4} + p^{5}

(2, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 4  3  2 4  3 4  p^{4}(p − 1)

(2, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 4  3 4  0

(2, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  2 4  0

h(2, 6, 6, 6, 4) = −p^{4} + p^{5}

(2, 6, 6, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  2 5 0

(2, 6, 6, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  3 3 0

(2, 6, 6, 7, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  3 4 0

(2, 6, 6, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  1 5  3 5 0

(2, 6, 7, 4, 1) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  1 1  p^{4}

h(2, 6, 7, 4, 1) = p^{4}

(2, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 3  2 2  −p^{4}(p − 1)

(2, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  1 2  0

h(2, 6, 7, 4, 2) = p^{4} − p^{5}

(2, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 3  2 3 −p^{4}(p − 1)

(2, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  1 3  p^{4}(p − 1)

cancel

(2, 6, 7, 4, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  1 4  p^{5}

h(2, 6, 7, 4, 4) = p^{5}

h(2, 6, 7, 5, 1) = p^{4}

\begin{matrix}(2, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 4  2 2 & 0 \\ (2, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  2 2 & 0 \\ (2, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  1 2 & 0 \end{matrix}

(2, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 4  2 3  0

(2, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  2 3  0

(2, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  1 3  p^{4}(p − 1)

h(2, 6, 7, 5, 3) = −p^{4} + p^{5}

\begin{matrix}(2, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 4  2 4 & 0 \\ (2, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  2 4 & 0 \\ (2, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  1 4 & 0 \end{matrix}

(2, 6, 7, 5, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  1 5  −p^{5}

h(2, 6, 7, 5, 5) = −p^{5}

(2, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 5  2 2  p^{4}(p − 1)

(2, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  2 2  0

h(2, 6, 7, 6, 2) = −p^{4} + p^{5}

(2, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 4  3 3  −p^{4}(p − 1)^{2} ; (2, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 5  2 3  0 ; (2, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  3 3  p^{5}(p − 1) ; (2, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  2 3  0 ; h(2, 6, 7, 6, 3) = −p^{4} + p^{5} (2, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 4  3 4  −p^{4}(p − 1)^{2} ; (2, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 5  2 4  p^{4}(p − 1)^{2} ; (2, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 4  3 4  p^{5}(p − 1) ; (2, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  2 4  0 ; h(2, 6, 7, 6, 4) = −p^{5} + p^{6}

503

(2, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 5  2 5  p^{5}(p − 1)
(2, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  2 5  0

h(2, 6, 7, 6, 5) = −p^{5} + p^{6}

(2, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 5  3 3 −p^{5}(p − 1)
(2, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  3 3  p^{5}(p − 1)

cancel

\begin{matrix}(2, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 5  3 4 & 0 \\ (2, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  3 4 & 0 \end{matrix}
(2, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  3  2 5  3 5  p^{5}(p − 1)
(2, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  3 5 −p^{5}(p − 1)

cancel

h(2, 6, 7, 8, 4) = −p^{6}

(2, 6, 7, 8, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  1 5  4 5  −p^{6}

h(2, 6, 7, 8, 5) = −p^{6}

(2, 6, 8, 5, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 4  2 2  p^{5}

h(2, 6, 8, 5, 2) = p^{5}

(2, 6, 8, 5, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 4  2 3 0

(2, 6, 8, 5, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 4  2 4  −p^{5}

h(2, 6, 8, 5, 4) = −p^{5}

(2, 6, 8, 6, 2) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 5  2 2  p^{5}

h(2, 6, 8, 6, 2) = p^{5}

\begin{matrix}(2, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 4  3 3 & 0 \\ (2, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 5  2 3 & 0 \end{matrix}

(2, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 4  3 4  0

(2, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 5  2 4  p^{5}(p − 1)

h(2, 6, 8, 6, 4) = −p^{5} + p^{6}

(2, 6, 8, 6, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 5  2 5  p^{6}

h(2, 6, 8, 6, 5) = p^{6}

(2, 6, 8, 7, 3) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 5  3 3 0

(2, 6, 8, 7, 4) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 5  3 4 0

(2, 6, 8, 7, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 5  3 5 0

h(2, 6, 8, 8, 4) = −p^{6}

(2, 6, 8, 8, 5) 5  4  3  2  1  0 5  4  2  1  0 5  4  2  1 5  4  2 5  4 5  −p^{6}

h(2, 6, 8, 8, 5) = −p^{6}

(3, 2, 1, 0, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 1  0 0  −p

h(3, 2, 1, 0, 0) = −p

(3, 2, 1, 0, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 1  0 1  −p

h(3, 2, 1, 0, 1) = −p

(3, 2, 1, 1, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 2  0 0 0

(3, 2, 1, 1, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 2  0 1 0

(3, 2, 1, 1, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 2  0 2 0

h(3, 2, 1, 2, 0) = p

(3, 2, 1, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 2  1 1  −p(p − 1)

(3, 2, 1, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 3  0 1  0

h(3, 2, 1, 2, 1) = p − p^{2}

(3, 2, 1, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 2  1 2 −p(p − 1)

(3, 2, 1, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 3  0 2  p(p − 1)

cancel

(3, 2, 1, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 3  0 3  p^{2}

h(3, 2, 1, 2, 3) = p^{2}

(3, 2, 1, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 3  1 1  −p^{2}

h(3, 2, 1, 3, 1) = −p^{2}

(3, 2, 1, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  1  0 3  1 2 0

h(3, 2, 1, 3, 3) = p^{2}

(3, 2, 2, 0, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 1  0 0  −p

h(3, 2, 2, 0, 0) = −p

(3, 2, 2, 0, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 1  0 1  −p

h(3, 2, 2, 0, 1) = −p

\begin{matrix}(3, 2, 2, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 2  0 0 & 0 \\ (3, 2, 2, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(3, 2, 2, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 2  0 1 & 0 \\ (3, 2, 2, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(3, 2, 2, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 2  0 2 & 0 \\ (3, 2, 2, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 2  0 2 & 0 \end{matrix}

(3, 2, 2, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  0 0  0

(3, 2, 2, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 3  0 0  −p(p − 1)

h(3, 2, 2, 2, 0) = p − p^{2}

(3, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 2  1 1  0

(3, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  0 1  0

(3, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 2  1 1  −p(p − 1)

(3, 2, 2, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 3  0 1  0

h(3, 2, 2, 2, 1) = p − p^{2}

(3, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  0 2  0

(3, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 2  1 2  −p(p − 1)

(3, 2, 2, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 3  0 2  −p(p − 1)^{2}

h(3, 2, 2, 2, 2) = p^{2} − p^{3}

(3, 2, 2, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  0 3  0

(3, 2, 2, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 3  0 3  −p^{2}(p − 1)

h(3, 2, 2, 2, 3) = p^{2} − p^{3}

(3, 2, 2, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 4  0 0  −p^{2}

h(3, 2, 2, 3, 0) = −p^{2}

\begin{matrix}(3, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  1 1 & 0 \\ (3, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 3  1 1 & 0 \\ (3, 2, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 4  0 1 & 0 \end{matrix}

(3, 2, 2, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  1 2  0

(3, 2, 2, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 3  1 2  0

(3, 2, 2, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 4  0 2  −p^{2}(p − 1)

h(3, 2, 2, 3, 2) = p^{2} − p^{3}

\begin{matrix}(3, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  1 3 & 0 \\ (3, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 3  1 3 & 0 \\ (3, 2, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 4  0 3 & 0 \end{matrix}

h(3, 2, 2, 3, 4) = p^{3}

(3, 2, 2, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 4  1 1  p^{2}

h(3, 2, 2, 4, 1) = p^{2}

\begin{matrix}(3, 2, 2, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  2 2 & 0 \\ (3, 2, 2, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 4  1 2 & 0 \end{matrix}

(3, 2, 2, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  0 3  2 3  0

(3, 2, 2, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 4  1 3  p^{2}(p − 1)

h(3, 2, 2, 4, 3) = −p^{2} + p^{3}

(3, 2, 2, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  1  0 4  1 4  p^{3}

h(3, 2, 2, 4, 4) = p^{3}

(3, 2, 3, 1, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 2  0 0 0

(3, 2, 3, 1, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 2  0 1 0

(3, 2, 3, 1, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 2  0 2 0

(3, 2, 3, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  0 0 0

(3, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  1 2  1 1  −p^{2}(p − 1)

(3, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 2  1 1  0

(3, 2, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  0 1  0

h(3, 2, 3, 2, 1) = p^{2} − p^{3}

(3, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 2  1 2  0

(3, 2, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  0 2  0

h(3, 2, 3, 2, 2) = p^{2} − p^{3}

(3, 2, 3, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  0 3 0

(3, 2, 3, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  0 0 0

(3, 2, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  1 3  1 1  −p^{2}(p − 1)

(3, 2, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  1 1  0

(3, 2, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  0 1  0

h(3, 2, 3, 3, 1) = p^{2} − p^{3}

\begin{matrix}(3, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  1 3  1 2 & 0 \\ (3, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  1 2 & 0 \\ (3, 2, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  0 2 & 0 \end{matrix}

(3, 2, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  1 3  1 3  p^{2}(p − 1)

(3, 2, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  1 3  0

(3, 2, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  0 3  0

h(3, 2, 3, 3, 3) = −p^{2} + p^{3}

(3, 2, 3, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  0 4 0

(3, 2, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  1 1 0

(3, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  2 2  0

(3, 2, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  1 2  0

h(3, 2, 3, 4, 2) = −p^{2} + p^{3}

(3, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 3  2  1 3  2 3  p^{2}(p − 1)

(3, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 3  2 3  0

(3, 2, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  1 3  0

h(3, 2, 3, 4, 3) = −p^{2} + p^{3}

(3, 2, 3, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  1 4 0

(3, 2, 3, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  2 2 0

(3, 2, 3, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  2 3 0

(3, 2, 3, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  0 4  2 4 0

(3, 2, 4, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  0 0  p^{2}

h(3, 2, 4, 2, 0) = p^{2}

(3, 2, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 2  1 1  −p^{2}(p − 1)

(3, 2, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  0 1  0

h(3, 2, 4, 2, 1) = p^{2} − p^{3}

(3, 2, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 2  1 2 −p^{2}(p − 1)

(3, 2, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  0 2  p^{2}(p − 1)

cancel

(3, 2, 4, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  0 3  p^{3}

h(3, 2, 4, 2, 3) = p^{3}

h(3, 2, 4, 3, 0) = p^{2}

\begin{matrix}(3, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 3  1 1 & 0 \\ (3, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  1 1 & 0 \\ (3, 2, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  0 1 & 0 \end{matrix}

(3, 2, 4, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 3  1 2  0

(3, 2, 4, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  1 2  0

(3, 2, 4, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  0 2  p^{2}(p − 1)

h(3, 2, 4, 3, 2) = −p^{2} + p^{3}

\begin{matrix}(3, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 3  1 3 & 0 \\ (3, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  1 3 & 0 \\ (3, 2, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  0 3 & 0 \end{matrix}

(3, 2, 4, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  0 4  −p^{3}

h(3, 2, 4, 3, 4) = −p^{3}

(3, 2, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 4  1 1  p^{2}(p − 1)

(3, 2, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  1 1  0

h(3, 2, 4, 4, 1) = −p^{2} + p^{3}

(3, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 3  2 2  −p^{2}(p − 1)^{2} ; (3, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 4  1 2  0 ; (3, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  2 2  p^{3}(p − 1) ; (3, 2, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  1 2  0 ; h(3, 2, 4, 4, 2) = −p^{2} + p^{3} (3, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 3  2 3  −p^{2}(p − 1)^{2} ; (3, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 4  1 3  p^{2}(p − 1)^{2} ; (3, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 3  2 3  p^{3}(p − 1) ; (3, 2, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  1 3  0 ; h(3, 2, 4, 4, 3) = −p^{3} + p^{4}

521

(3, 2, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 4  1 4  p^{3}(p − 1)
(3, 2, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  1 4  0

h(3, 2, 4, 4, 4) = −p^{3} + p^{4}

(3, 2, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 4  2 2 −p^{3}(p − 1)
(3, 2, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  2 2  p^{3}(p − 1)

cancel

\begin{matrix}(3, 2, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 4  2 3 & 0 \\ (3, 2, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  2 3 & 0 \end{matrix}
(3, 2, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  2  1 4  2 4  p^{3}(p − 1)
(3, 2, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  2 4 −p^{3}(p − 1)

cancel

h(3, 2, 4, 6, 3) = −p^{4}

(3, 2, 4, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  0 4  3 4  −p^{4}

h(3, 2, 4, 6, 4) = −p^{4}

(3, 2, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 3  1 1  p^{3}

h(3, 2, 5, 3, 1) = p^{3}

(3, 2, 5, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 3  1 2 0

(3, 2, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 3  1 3  −p^{3}

h(3, 2, 5, 3, 3) = −p^{3}

(3, 2, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 4  1 1  p^{3}

h(3, 2, 5, 4, 1) = p^{3}

\begin{matrix}(3, 2, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 3  2 2 & 0 \\ (3, 2, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 4  1 2 & 0 \end{matrix}

(3, 2, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 3  2 3  0

(3, 2, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 4  1 3  p^{3}(p − 1)

h(3, 2, 5, 4, 3) = −p^{3} + p^{4}

(3, 2, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 4  1 4  p^{4}

h(3, 2, 5, 4, 4) = p^{4}

(3, 2, 5, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 4  2 2 0

(3, 2, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 4  2 3 0

(3, 2, 5, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 4  2 4 0

h(3, 2, 5, 6, 3) = −p^{4}

(3, 2, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  1  0 4  3  1 4  3 4  −p^{4}

h(3, 2, 5, 6, 4) = −p^{4}

(3, 3, 1, 0, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 1  0 0  −p

h(3, 3, 1, 0, 0) = −p

(3, 3, 1, 0, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 1  0 1  −p

h(3, 3, 1, 0, 1) = −p

(3, 3, 1, 1, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 2  0 0 0

(3, 3, 1, 1, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 2  0 1 0

(3, 3, 1, 1, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 2  0 2 0

h(3, 3, 1, 2, 0) = p

(3, 3, 1, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 2  1 1  −p(p − 1)

(3, 3, 1, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 3  0 1  0

h(3, 3, 1, 2, 1) = p − p^{2}

(3, 3, 1, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 2  1 2 −p(p − 1)

(3, 3, 1, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 3  0 2  p(p − 1)

cancel

(3, 3, 1, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 3  0 3  p^{2}

h(3, 3, 1, 2, 3) = p^{2}

(3, 3, 1, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 3  1 1  −p^{2}

h(3, 3, 1, 3, 1) = −p^{2}

(3, 3, 1, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  1  0 3  1 2 0

h(3, 3, 1, 3, 3) = p^{2}

(3, 3, 2, 0, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 1  0 0 0

(3, 3, 2, 0, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 1  0 1 0

\begin{matrix}(3, 3, 2, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 2  0 0 & 0 \\ (3, 3, 2, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 2  0 0 & 0 \\ (3, 3, 2, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(3, 3, 2, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 2  0 1 & 0 \\ (3, 3, 2, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 2  0 1 & 0 \\ (3, 3, 2, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(3, 3, 2, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 2  0 2 & 0 \\ (3, 3, 2, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 2  0 2 & 0 \\ (3, 3, 2, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 2  0 2 & 0 \end{matrix} \begin{matrix}(3, 3, 2, 2, 0) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  0 0 & 0 \\ (3, 3, 2, 2, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  0 0 & 0 \\ (3, 3, 2, 2, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 3  0 0 & 0 \end{matrix}

528

\begin{matrix}(3, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 2  1 1 & 0 \\ (3, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  0 1 & 0 \\ (3, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 2  1 1 & 0 \\ (3, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  0 1 & 0 \\ (3, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 2  1 1 & 0 \\ (3, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 3  0 1 & 0 \end{matrix}

529

\begin{matrix}(3, 3, 2, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 2  1 2 & 0 \\ (3, 3, 2, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  0 2 & 0 \\ (3, 3, 2, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 2  1 2 & 0 \\ (3, 3, 2, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  0 2 & 0 \\ (3, 3, 2, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 2  1 2 & 0 \\ (3, 3, 2, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 3  0 2 & 0 \end{matrix} \begin{matrix}(3, 3, 2, 2, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  0 3 & 0 \\ (3, 3, 2, 2, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  0 3 & 0 \\ (3, 3, 2, 2, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 3  0 3 & 0 \end{matrix}

530

(3, 3, 2, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  0 0 0

\begin{matrix}(3, 3, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  1 1 & 0 \\ (3, 3, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  1 1 & 0 \\ (3, 3, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 3  1 1 & 0 \\ (3, 3, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  0 1 & 0 \end{matrix}

\begin{matrix}(3, 3, 2, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  1 2 & 0 \\ (3, 3, 2, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  1 2 & 0 \\ (3, 3, 2, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 3  1 2 & 0 \\ (3, 3, 2, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  0 2 & 0 \end{matrix}

\begin{matrix}(3, 3, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  1 3 & 0 \\ (3, 3, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  1 3 & 0 \\ (3, 3, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 3  1 3 & 0 \\ (3, 3, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  0 3 & 0 \end{matrix}

(3, 3, 2, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  0 4 0

(3, 3, 2, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  1 1 0

\begin{matrix}(3, 3, 2, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  2 2 & 0 \\ (3, 3, 2, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  2 2 & 0 \\ (3, 3, 2, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(3, 3, 2, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  0 3  2 3 & 0 \\ (3, 3, 2, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  0 3  2 3 & 0 \\ (3, 3, 2, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  1 3 & 0 \end{matrix}

(3, 3, 2, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  1  0 4  1 4 0

(3, 3, 3, 0, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 1  0 0  p

h(3, 3, 3, 0, 0) = p

(3, 3, 3, 0, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 1  0 1  p

h(3, 3, 3, 0, 1) = p

\begin{matrix}(3, 3, 3, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 2  0 0 & 0 \\ (3, 3, 3, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 2  0 0 & 0 \\ (3, 3, 3, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(3, 3, 3, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 2  0 1 & 0 \\ (3, 3, 3, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 2  0 1 & 0 \\ (3, 3, 3, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(3, 3, 3, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 2  0 2 & 0 \\ (3, 3, 3, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 2  0 2 & 0 \\ (3, 3, 3, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 2  0 2 & 0 \end{matrix}

(3, 3, 3, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  0 0  0

(3, 3, 3, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 3  0 0  p(p − 1)

h(3, 3, 3, 2, 0) = −p + p^{2}

(3, 3, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 2  1 1  0

(3, 3, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 3  0 1  0

(3, 3, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  1 2  1 1  −p^{2}(p − 1)

(3, 3, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 2  1 1  0

(3, 3, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  0 1  0

(3, 3, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 2  1 1  p(p − 1)

(3, 3, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 3  0 1  0

h(3, 3, 3, 2, 1) = −p + 2p^{2} − p^{3}

(3, 3, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  1 2  1 2  0
(3, 3, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 2  1 2  0
(3, 3, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 3  0 2  0
(3, 3, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  1 2  1 2 −p^{2}(p − 1)
(3, 3, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 2  1 2  0
(3, 3, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  0 2  0
(3, 3, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 2  1 2  p(p − 1)
(3, 3, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 3  0 2  p(p − 1)^{2}

cancel

(3, 3, 3, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 3  0 3  0 ; (3, 3, 3, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  0 3  0 ; (3, 3, 3, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 3  0 3  p^{2}(p − 1) ; h(3, 3, 3, 2, 3) = −p^{2} + p^{3} \begin{matrix}(3, 3, 3, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  0 0 & 0 \\ (3, 3, 3, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  0 0 & 0 \\ (3, 3, 3, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  0 0 & 0 \end{matrix}

538

(3, 3, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 3  1 1  0

(3, 3, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  0 1  0

(3, 3, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  1 3  1 1  −p^{2}(p − 1)

(3, 3, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  1 1  0

(3, 3, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  0 1  0

(3, 3, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 3  1 1  0

(3, 3, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  0 1  0

h(3, 3, 3, 3, 1) = p^{2} − p^{3}

\begin{matrix}(3, 3, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  1 3  1 2 & 0 \\ (3, 3, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 3  1 2 & 0 \\ (3, 3, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  0 2 & 0 \\ (3, 3, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  1 3  1 2 & 0 \\ (3, 3, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  1 2 & 0 \\ (3, 3, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  0 2 & 0 \\ (3, 3, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 3  1 2 & 0 \\ (3, 3, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  0 2 & 0 \end{matrix}

540

(3, 3, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 3  1 3  0

(3, 3, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  0 3  0

(3, 3, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  1 3  1 3  p^{2}(p − 1)

(3, 3, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  1 3  0

(3, 3, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  0 3  0

(3, 3, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 3  1 3  0

(3, 3, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  0 3  0

h(3, 3, 3, 3, 3) = −p^{2} + p^{3}

\begin{matrix}(3, 3, 3, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  0 4 & 0 \\ (3, 3, 3, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  0 4 & 0 \\ (3, 3, 3, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  0 4 & 0 \end{matrix}

(3, 3, 3, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  0 0  −p^{2}

h(3, 3, 3, 4, 0) = −p^{2}

(3, 3, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  1 1  0

(3, 3, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  1 1  0

(3, 3, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  1 1  p^{2}(p − 1)

(3, 3, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  0 1  0

h(3, 3, 3, 4, 1) = −p^{2} + p^{3}

(3, 3, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 3  2  1 3  2 2  0
(3, 3, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 3  2 2  0
(3, 3, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  1 2  0
(3, 3, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  1 3  2 2  p^{2}(p − 1)
(3, 3, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  2 2  0
(3, 3, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  1 2  0
(3, 3, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  1 2  0
(3, 3, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  0 2 −p^{2}(p − 1)

canceel

(3, 3, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 3  2 3  0

(3, 3, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  1 3  0

(3, 3, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 3  2  1 3  2 3  p^{2}(p − 1)

(3, 3, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 3  2 3  0

(3, 3, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  1 3  0

(3, 3, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  1 3  p^{2}(p − 1)^{2}

(3, 3, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  0 3  0

h(3, 3, 3, 4, 3) = −p^{3} + p^{4}

(3, 3, 3, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  1 4  0

(3, 3, 3, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 4  1 4  p^{3}(p − 1)

(3, 3, 3, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  0 4 −p^{3}(p − 1)

cancel

(3, 3, 3, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  0 5  −p^{4}

h(3, 3, 3, 4, 5) = −p^{4}

(3, 3, 3, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  1 1  p^{3}

h(3, 3, 3, 5, 1) = p^{3}

\begin{matrix}(3, 3, 3, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  2 2 & 0 \\ (3, 3, 3, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  2 2 & 0 \\ (3, 3, 3, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  1 2 & 0 \end{matrix}

(3, 3, 3, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  2 3  0

(3, 3, 3, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  2 3  0

(3, 3, 3, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  1 3  p^{3}(p − 1)

h(3, 3, 3, 5, 3) = −p^{3} + p^{4}

\begin{matrix}(3, 3, 3, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  0 4  2 4 & 0 \\ (3, 3, 3, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  0 4  2 4 & 0 \\ (3, 3, 3, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  1  0 5  1 4 & 0 \end{matrix}

h(3, 3, 3, 5, 5) = −p^{4}

(3, 3, 4, 1, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 2  0 0 0

(3, 3, 4, 1, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 2  0 1 0

(3, 3, 4, 1, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 2  0 2 0

\begin{matrix}(3, 3, 4, 2, 0) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  0 0 & 0 \\ (3, 3, 4, 2, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  0 0 & 0 \\ (3, 3, 4, 2, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  0 0 & 0 \end{matrix}

\begin{matrix}(3, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 2  1 1 & 0 \\ (3, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  0 1 & 0 \\ (3, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 2  1 1 & 0 \\ (3, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  0 1 & 0 \\ (3, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 2  1 1 & 0 \\ (3, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  0 1 & 0 \end{matrix}

548

\begin{matrix}(3, 3, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 2  1 2 & 0 \\ (3, 3, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  0 2 & 0 \\ (3, 3, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 2  1 2 & 0 \\ (3, 3, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  0 2 & 0 \\ (3, 3, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 2  1 2 & 0 \\ (3, 3, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  0 2 & 0 \end{matrix} \begin{matrix}(3, 3, 4, 2, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  0 3 & 0 \\ (3, 3, 4, 2, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  0 3 & 0 \\ (3, 3, 4, 2, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  0 3 & 0 \end{matrix}

549

\begin{matrix}(3, 3, 4, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  0 0 & 0 \\ (3, 3, 4, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  0 0 & 0 \\ (3, 3, 4, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  0 0 & 0 \end{matrix}

550

\begin{matrix}(3, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 3  1 1 & 0 \\ (3, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  1 1 & 0 \\ (3, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  0 1 & 0 \\ (3, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 3  1 1 & 0 \\ (3, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  1 1 & 0 \\ (3, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  0 1 & 0 \\ (3, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  1 1 & 0 \\ (3, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  0 1 & 0 \end{matrix}

551

\begin{matrix}(3, 3, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 3  1 2 & 0 \\ (3, 3, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  1 2 & 0 \\ (3, 3, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  0 2 & 0 \\ (3, 3, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 3  1 2 & 0 \\ (3, 3, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  1 2 & 0 \\ (3, 3, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  0 2 & 0 \\ (3, 3, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  1 2 & 0 \\ (3, 3, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  0 2 & 0 \end{matrix}

552

\begin{matrix}(3, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 3  1 3 & 0 \\ (3, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  1 3 & 0 \\ (3, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  0 3 & 0 \\ (3, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 3  1 3 & 0 \\ (3, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  1 3 & 0 \\ (3, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  0 3 & 0 \\ (3, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  1 3 & 0 \\ (3, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  0 3 & 0 \end{matrix}

553

\begin{matrix}(3, 3, 4, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  0 4 & 0 \\ (3, 3, 4, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  0 4 & 0 \\ (3, 3, 4, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  0 4 & 0 \end{matrix} (3, 3, 4, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  0 0 0

554

\begin{matrix}(3, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 4  1 1 & 0 \\ (3, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  1 1 & 0 \\ (3, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 4  1 1 & 0 \\ (3, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  1 1 & 0 \\ (3, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  1 1 & 0 \\ (3, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  0 1 & 0 \end{matrix}

555

\begin{matrix}(3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 3  2 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 4  1 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  2 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  1 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 3  2 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 4  1 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  2 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  1 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  2 2 & 0 \end{matrix}

556

\begin{matrix}(3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  1 2 & 0 \\ (3, 3, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  0 2 & 0 \end{matrix}

557

\begin{matrix}(3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 3  2 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 4  1 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 3  2 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  1 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 3  2 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 4  1 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 3  2 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  1 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 3  2 3 & 0 \end{matrix}

558

\begin{matrix}(3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  1 3 & 0 \\ (3, 3, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  0 3 & 0 \end{matrix}

\begin{matrix}(3, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 4  1 4 & 0 \\ (3, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  1 4 & 0 \\ (3, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 4  1 4 & 0 \\ (3, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  1 4 & 0 \\ (3, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  1 4 & 0 \\ (3, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  0 4 & 0 \end{matrix}

(3, 3, 4, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  0 5 0

(3, 3, 4, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  1 1 0 \begin{matrix}(3, 3, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 4  2 2 & 0 \\ (3, 3, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  2 2 & 0 \\ (3, 3, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 4  2 2 & 0 \\ (3, 3, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  2 2 & 0 \\ (3, 3, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  2 2 & 0 \\ (3, 3, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  1 2 & 0 \end{matrix}

560

\begin{matrix}(3, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 4  2 3 & 0 \\ (3, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  2 3 & 0 \\ (3, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 4  2 3 & 0 \\ (3, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  2 3 & 0 \\ (3, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  2 3 & 0 \\ (3, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  1 3 & 0 \end{matrix}

561

\begin{matrix}(3, 3, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  2  1 4  2 4 & 0 \\ (3, 3, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  2 4 & 0 \\ (3, 3, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  2  1 4  2 4 & 0 \\ (3, 3, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  2 4 & 0 \\ (3, 3, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 4  2 4 & 0 \\ (3, 3, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  1 4 & 0 \end{matrix}

(3, 3, 4, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  1 5 0

(3, 3, 4, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  2 2 0

\begin{matrix}(3, 3, 4, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  3 3 & 0 \\ (3, 3, 4, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  3 3 & 0 \\ (3, 3, 4, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  2 3 & 0 \end{matrix}

\begin{matrix}(3, 3, 4, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  0 4  3 4 & 0 \\ (3, 3, 4, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  0 4  3 4 & 0 \\ (3, 3, 4, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  2 4 & 0 \end{matrix}

(3, 3, 4, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  0 5  2 5 0

(3, 3, 5, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  0 0  −p^{2}

h(3, 3, 5, 2, 0) = −p^{2}

(3, 3, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  0 1  0

h(3, 3, 5, 2, 1) = −p^{2} + p^{3}

(3, 3, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 2  1 2  p^{2}(p − 1)

(3, 3, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  0 2 −p^{2}(p − 1)

cancel

(3, 3, 5, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  0 3  −p^{3}

h(3, 3, 5, 2, 3) = −p^{3}

(3, 3, 5, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  0 0 0

(3, 3, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 3  1 1  −p^{3}(p − 1)

(3, 3, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 3  1 1  0

(3, 3, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  1 1  0

(3, 3, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  0 1  0

h(3, 3, 5, 3, 1) = p^{3} − p^{4}

\begin{matrix}(3, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  1 3  1 2 & 0 \\ (3, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 3  1 2 & 0 \\ (3, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 3  1 2 & 0 \\ (3, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  1 2 & 0 \\ (3, 3, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  0 2 & 0 \end{matrix}

566

(3, 3, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 3  1 3  p^{3}(p − 1)

(3, 3, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 3  1 3  0

(3, 3, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  1 3  0

(3, 3, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  0 3  0

h(3, 3, 5, 3, 3) = −p^{3} + p^{4}

(3, 3, 5, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  0 4 0

(3, 3, 5, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  0 0  p^{2}

h(3, 3, 5, 4, 0) = p^{2}

(3, 3, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  1 1  −p^{3}(p − 1)

(3, 3, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 4  1 1  p^{2}(p − 1)^{2}

(3, 3, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  1 1  0

(3, 3, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  0 1  0

h(3, 3, 5, 4, 1) = p^{2} − p^{3}

(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  1 3  2 2  0
(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  1 4  1 2  0
(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 3  2 2  0
(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  1 2  0
(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 3  2 2  p^{2}(p − 1)^{2}
(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 4  1 2  0
(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  2 2 −p^{3}(p − 1)
(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  1 2  0
(3, 3, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  0 2  p^{2}(p − 1)

cancel

(3, 3, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  1 4  1 3  0

(3, 3, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 3  2 3  0

(3, 3, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  1 3  −p^{3}(p − 1)^{2}

(3, 3, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 3  2 3  p^{2}(p − 1)^{2}

(3, 3, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 4  1 3  p^{2}(p − 1)^{3}

(3, 3, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 3  2 3  −p^{3}(p − 1)

(3, 3, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  1 3  0

(3, 3, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  0 3  0

h(3, 3, 5, 4, 3) = p^{3} − p^{4}

\begin{matrix}(3, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  1 4  1 4 & 0 \\ (3, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  1 4 & −p^{4}(p − 1) \\ (3, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 4  1 4 & p^{3}(p − 1)^{2} \\ (3, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  1 4 & 0 \\ (3, 3, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  0 4 & p^{3}(p − 1) \end{matrix}

(3, 3, 5, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  0 5  p^{4}

h(3, 3, 5, 4, 5) = p^{4}

(3, 3, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  1 1  p^{3}(p − 1)

(3, 3, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  1 1  0

h(3, 3, 5, 5, 1) = −p^{3} + p^{4}

\begin{matrix}(3, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  1 4  2 2 & 0 \\ (3, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  2 2 & 0 \\ (3, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 4  2 2 & 0 \\ (3, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  1 2 & 0 \\ (3, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  2 2 & 0 \\ (3, 3, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  1 2 & 0 \end{matrix}

572

(3, 3, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  2 3  0

(3, 3, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 4  2 3  0

(3, 3, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  1 3  p^{3}(p − 1)^{2}

(3, 3, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  2 3  0

(3, 3, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  1 3  0

h(3, 3, 5, 5, 3) = p^{3} − 2p^{4} + p^{5}

\begin{matrix}(3, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  1 4  2 4 & 0 \\ (3, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  2 4 & 0 \\ (3, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 4  2 4 & 0 \\ (3, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  1 4 & 0 \\ (3, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  2 4 & 0 \\ (3, 3, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  1 4 & 0 \end{matrix} (3, 3, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  1 5  −p^{4}(p − 1) ; (3, 3, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  1 5  0 ; h(3, 3, 5, 5, 5) = p^{4} − p^{5}

574

(3, 3, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  2 2 −p^{3}(p − 1)
(3, 3, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  2 2  p^{3}(p − 1)

cancel

(3, 3, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  1 4  3 3  0
(3, 3, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  3 3  p^{4}(p − 1)
(3, 3, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  2 3  0
(3, 3, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  3 3 −p^{4}(p − 1)
(3, 3, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  2 3  0

cancel

(3, 3, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 4  3  1 4  3 4  p^{4}(p − 1)

(3, 3, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  2 4 −p^{3}(p − 1)^{2}

(3, 3, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 4  3 4  −p^{4}(p − 1)

(3, 3, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  2 4  p^{3}(p − 1)^{2}

cancel

(3, 3, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  2  1 5  2 5 −p^{4}(p − 1)

(3, 3, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  2 5  p^{4}(p − 1)

cancel

(3, 3, 5, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  3 3  −p^{5}

h(3, 3, 5, 7, 3) = −p^{5}

(3, 3, 5, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  3 4 0

(3, 3, 5, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  0 5  3 5  p^{5}

h(3, 3, 5, 7, 5) = p^{5}

(3, 3, 6, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 3  1 1  −p^{4}

h(3, 3, 6, 3, 1) = −p^{4}

(3, 3, 6, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 3  1 2 0

(3, 3, 6, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 3  1 3  p^{4}

h(3, 3, 6, 3, 3) = p^{4}

(3, 3, 6, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  1 1 0

\begin{matrix}(3, 3, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  2 3  2 2 & 0 \\ (3, 3, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 3  2 2 & 0 \\ (3, 3, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(3, 3, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  2 3  2 3 & 0 \\ (3, 3, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 3  2 3 & 0 \\ (3, 3, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  1 3 & 0 \end{matrix}

(3, 3, 6, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  1 4 0

(3, 3, 6, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  1 1  p^{4}

h(3, 3, 6, 5, 1) = p^{4}

\begin{matrix}(3, 3, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  2 4  2 2 & 0 \\ (3, 3, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  2 2 & 0 \\ (3, 3, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  1 2 & 0 \end{matrix}

(3, 3, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  2 4  2 3  0

(3, 3, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  2 3  0

(3, 3, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  1 3  p^{4}(p − 1)

h(3, 3, 6, 5, 3) = −p^{4} + p^{5}

\begin{matrix}(3, 3, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  2 4  2 4 & 0 \\ (3, 3, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  2 4 & 0 \\ (3, 3, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  1 4 & 0 \end{matrix}

h(3, 3, 6, 5, 5) = −p^{5}

(3, 3, 6, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  2 2 0

\begin{matrix}(3, 3, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  2 4  3 3 & 0 \\ (3, 3, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  3 3 & 0 \\ (3, 3, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  2 3 & 0 \end{matrix}

\begin{matrix}(3, 3, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  0 4  3  2 4  3 4 & 0 \\ (3, 3, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 4  3 4 & 0 \\ (3, 3, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  2 4 & 0 \end{matrix}

(3, 3, 6, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  2 5 0

h(3, 3, 6, 7, 3) = −p^{5}

(3, 3, 6, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  3 4 0

(3, 3, 6, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  1  0 5  3  1 5  3 5  p^{5}

h(3, 3, 6, 7, 5) = p^{5}

(3, 4, 2, 0, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 1  0 0  p

h(3, 4, 2, 0, 0) = p

(3, 4, 2, 0, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 1  0 1  p

h(3, 4, 2, 0, 1) = p

\begin{matrix}(3, 4, 2, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 2  0 0 & 0 \\ (3, 4, 2, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(3, 4, 2, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 2  0 1 & 0 \\ (3, 4, 2, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(3, 4, 2, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 2  0 2 & 0 \\ (3, 4, 2, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 2  0 2 & 0 \end{matrix}

(3, 4, 2, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 3  0 0  0

(3, 4, 2, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 3  0 0  p(p − 1)

h(3, 4, 2, 2, 0) = −p + p^{2}

(3, 4, 2, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 2  1 1  0 ; (3, 4, 2, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 3  0 1  0 ; (3, 4, 2, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 2  1 1  p(p − 1) ; (3, 4, 2, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 3  0 1  0 ; h(3, 4, 2, 2, 1) = −p + p^{2} (3, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 2  1 2  0 ; (3, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 3  0 2  0 ; (3, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 2  1 2  p(p − 1) ; (3, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 3  0 2  p(p − 1)^{2} ; h(3, 4, 2, 2, 2) = −p^{2} + p^{3}

583

(3, 4, 2, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 3  0 3  p^{2}(p − 1)

h(3, 4, 2, 2, 3) = −p^{2} + p^{3}

(3, 4, 2, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  0 0  p^{2}

h(3, 4, 2, 3, 0) = p^{2}

\begin{matrix}(3, 4, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 3  1 1 & 0 \\ (3, 4, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 3  1 1 & 0 \\ (3, 4, 2, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  0 1 & 0 \end{matrix}

(3, 4, 2, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 3  1 2  0

(3, 4, 2, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  0 2  p^{2}(p − 1)

h(3, 4, 2, 3, 2) = −p^{2} + p^{3}

\begin{matrix}(3, 4, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 3  1 3 & 0 \\ (3, 4, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 3  1 3 & 0 \\ (3, 4, 2, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  0 3 & 0 \end{matrix}

(3, 4, 2, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  0 4  −p^{3}

h(3, 4, 2, 3, 4) = −p^{3}

(3, 4, 2, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  1 1  −p^{2}

h(3, 4, 2, 4, 1) = −p^{2}

\begin{matrix}(3, 4, 2, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 3  2 2 & 0 \\ (3, 4, 2, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  1 2 & 0 \end{matrix}

(3, 4, 2, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  0 3  2 3  0

(3, 4, 2, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  1 3  −p^{2}(p − 1)

h(3, 4, 2, 4, 3) = p^{2} − p^{3}

(3, 4, 2, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  1  0 4  1 4  −p^{3}

h(3, 4, 2, 4, 4) = −p^{3}

(3, 4, 3, 0, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 1  0 0  p

h(3, 4, 3, 0, 0) = p

(3, 4, 3, 0, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 1  0 1  p

h(3, 4, 3, 0, 1) = p

\begin{matrix}(3, 4, 3, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 2  0 0 & 0 \\ (3, 4, 3, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 2  0 0 & 0 \\ (3, 4, 3, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(3, 4, 3, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 2  0 1 & 0 \\ (3, 4, 3, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 2  0 1 & 0 \\ (3, 4, 3, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(3, 4, 3, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 2  0 2 & 0 \\ (3, 4, 3, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 2  0 2 & 0 \\ (3, 4, 3, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 2  0 2 & 0 \end{matrix}

(3, 4, 3, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  0 0  0

(3, 4, 3, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 3  0 0  p(p − 1)

h(3, 4, 3, 2, 0) = −p + p^{2}

(3, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  1 2  1 1  0

(3, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 2  1 1  0

(3, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 3  0 1  0

(3, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 2  1 1  0

(3, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  0 1  0

(3, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 2  1 1  p(p − 1)

(3, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 3  0 1  0

h(3, 4, 3, 2, 1) = −p + p^{2} + p^{3} − p^{4}

(3, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  1 2  1 2  0

(3, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 2  1 2  0

(3, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 3  0 2  0

(3, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 2  1 2  0

(3, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  0 2  0

(3, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 2  1 2  p(p − 1)

(3, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 3  0 2  p(p − 1)^{2}

h(3, 4, 3, 2, 2) = −p^{2} + 2p^{3} − p^{4}

(3, 4, 3, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 3  0 3  0 ; (3, 4, 3, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  0 3  0 ; (3, 4, 3, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 3  0 3  p^{2}(p − 1) ; h(3, 4, 3, 2, 3) = −p^{2} + p^{3} \begin{matrix}(3, 4, 3, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  0 0 & 0 \\ (3, 4, 3, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  0 0 & 0 \\ (3, 4, 3, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  0 0 & 0 \end{matrix}

591

(3, 4, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  1 3  1 1  0

(3, 4, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 3  1 1  0

(3, 4, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  0 1  0

(3, 4, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  1 1  0

(3, 4, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  0 1  0

(3, 4, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 3  1 1  0

(3, 4, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  0 1  0

h(3, 4, 3, 3, 1) = p^{3} − p^{4}

\begin{matrix}(3, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 3  2  1 3  1 2 & 0 \\ (3, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  1 3  1 2 & 0 \\ (3, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 3  1 2 & 0 \\ (3, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  0 2 & 0 \\ (3, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  1 2 & 0 \\ (3, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  0 2 & 0 \\ (3, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 3  1 2 & 0 \\ (3, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  0 2 & 0 \end{matrix}

593

(3, 4, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  1 3  1 3  0

(3, 4, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 3  1 3  0

(3, 4, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  0 3  0

(3, 4, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  1 3  0

(3, 4, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  0 3  0

(3, 4, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 3  1 3  0

(3, 4, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  0 3  0

h(3, 4, 3, 3, 3) = −p^{3} + p^{4}

\begin{matrix}(3, 4, 3, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  0 4 & 0 \\ (3, 4, 3, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  0 4 & 0 \\ (3, 4, 3, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  0 4 & 0 \end{matrix}

(3, 4, 3, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  0 0  −p^{2}

h(3, 4, 3, 4, 0) = −p^{2}

(3, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  1 1  0

(3, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  1 1  0

(3, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  1 1  p^{2}(p − 1)

(3, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  0 1  0

h(3, 4, 3, 4, 1) = −p^{2} + p^{3}

(3, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  1 3  2 2  0

(3, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 3  2 2  0

(3, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  1 2  0

(3, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  2 2  0

(3, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  1 2  0

(3, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  1 2  0

(3, 4, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  0 2  −p^{2}(p − 1)

h(3, 4, 3, 4, 2) = p^{2} − 2p^{3} + p^{4}

(3, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 3  2  1 3  2 3  0

(3, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 3  2 3  0

(3, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  1 3  0

(3, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 3  2 3  0

(3, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  1 3  0

(3, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  1 3  p^{2}(p − 1)^{2}

(3, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  0 3  0

h(3, 4, 3, 4, 3) = p^{2} − 3p^{3} + 2p^{4}

(3, 4, 3, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  1 4  0

(3, 4, 3, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 4  1 4  p^{3}(p − 1)

(3, 4, 3, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  0 4 −p^{3}(p − 1)

cancel

(3, 4, 3, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  0 5  −p^{4}

h(3, 4, 3, 4, 5) = −p^{4}

(3, 4, 3, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  1 1  p^{3}

h(3, 4, 3, 5, 1) = p^{3}

\begin{matrix}(3, 4, 3, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  2 2 & 0 \\ (3, 4, 3, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  2 2 & 0 \\ (3, 4, 3, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  1 2 & 0 \end{matrix}

(3, 4, 3, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  2 3  0

(3, 4, 3, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  2 3  0

(3, 4, 3, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  1 3  p^{3}(p − 1)

h(3, 4, 3, 5, 3) = −p^{3} + p^{4}

\begin{matrix}(3, 4, 3, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  0 4  2 4 & 0 \\ (3, 4, 3, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  0 4  2 4 & 0 \\ (3, 4, 3, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  1  0 5  1 4 & 0 \end{matrix}

h(3, 4, 3, 5, 5) = −p^{4}

\begin{matrix}(3, 4, 4, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 2  0 0 & 0 \\ (3, 4, 4, 1, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 2  0 0 & 0 \end{matrix}

\begin{matrix}(3, 4, 4, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 2  0 1 & 0 \\ (3, 4, 4, 1, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 2  0 1 & 0 \end{matrix}

\begin{matrix}(3, 4, 4, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 2  0 2 & 0 \\ (3, 4, 4, 1, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 2  0 2 & 0 \end{matrix}

(3, 4, 4, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  0 0  0

(3, 4, 4, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  0 0  p^{2}(p − 1)

(3, 4, 4, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 3  0 0  0

h(3, 4, 4, 2, 0) = −p^{2} + p^{3}

(3, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 2  1 1  0

(3, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 3  0 1  0

(3, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 2  1 1  0

(3, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  0 1  0

(3, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 2  1 1  p^{2}(p − 1)

(3, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  0 1  0

(3, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 2  1 1  0

(3, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 3  0 1  0

h(3, 4, 4, 2, 1) = −p^{2} + 2p^{3} − p^{4}

(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 2  1 2 −p^{3}(p − 1)
(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 2  1 2  0
(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 3  0 2  0
(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 2  1 2  0
(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  0 2  0
(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 2  1 2  p^{2}(p − 1)
(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  0 2  p^{2}(p − 1)^{2}
(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 2  1 2  0
(3, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 3  0 2  0

cancel

(3, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 3  0 3  0 ; (3, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  0 3  0 ; (3, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  0 3  p^{3}(p − 1) ; (3, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 3  0 3  0 ; h(3, 4, 4, 2, 3) = −p^{3} + p^{4} (3, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  0 0  0 ; (3, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  0 0  0 ; (3, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  0 0  p^{2}(p − 1) ; (3, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  0 0  0 ; h(3, 4, 4, 3, 0) = −p^{2} + p^{3}

604

\begin{matrix}(3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 3  1 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 3  1 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 3  1 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  0 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  1 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  0 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 3  1 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  1 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  0 1 & 0 \end{matrix}

605

\begin{matrix}(3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 3  1 1 & 0 \\ (3, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  0 1 & 0 \end{matrix}

606

\begin{matrix}(3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 3  1 2 & 0 \\ (3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 3  1 2 & 0 \\ (3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 3  1 2 & 0 \\ (3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  0 2 & 0 \\ (3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  1 2 & 0 \\ (3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  0 2 & 0 \\ (3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 3  1 2 & 0 \\ (3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  1 2 & 0 \\ (3, 4, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  0 2 & p^{2}(p − 1)^{2} \end{matrix}

607

(3, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  0 2  0

h(3, 4, 4, 3, 2) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 3  1 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 3  1 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 3  1 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  0 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  1 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  0 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 3  1 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  1 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  0 3 & 0 \end{matrix}

609

\begin{matrix}(3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 3  1 3 & 0 \\ (3, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  0 3 & 0 \end{matrix}

(3, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  0 4  0

(3, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  0 4  0

(3, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  0 4  −p^{3}(p − 1)

(3, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  0 4  0

h(3, 4, 4, 3, 4) = p^{3} − p^{4}

\begin{matrix}(3, 4, 4, 4, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  0 0 & 0 \\ (3, 4, 4, 4, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  0 0 & 0 \end{matrix}

(3, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 4  1 1  0

(3, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  1 1  0

(3, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  1 1  0

(3, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  0 1  0

(3, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 4  1 1  −p^{2}(p − 1)

(3, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  1 1  0

(3, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  1 1  0

(3, 4, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  0 1  0

h(3, 4, 4, 4, 1) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 3  2 2 & −p^{3}(p − 1)^{2} \\ (3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 4  1 2 & 0 \\ (3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 3  2 2 & 0 \\ (3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 4  1 2 & 0 \\ (3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 3  2 2 & 0 \\ (3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  1 2 & 0 \\ (3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  2 2 & 0 \\ (3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  1 2 & 0 \\ (3, 4, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  0 2 & 0 \end{matrix}

612

(3, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 4  1 2  0

(3, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  2 2  p^{3}(p − 1)^{2}

(3, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  1 2  0

(3, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 3  2 2  0

(3, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  1 2  0

(3, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  0 2  0

h(3, 4, 4, 4, 2) = p^{2} − 2p^{3} + p^{4}

\begin{matrix}(3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 3  2 3 & −p^{3}(p − 1)^{2} \\ (3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 4  1 3 & p^{3}(p − 1)^{2} \\ (3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 3  2 3 & 0 \\ (3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 4  1 3 & 0 \\ (3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 3  2 3 & 0 \\ (3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  1 3 & 0 \\ (3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 3  2 3 & 0 \\ (3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  1 3 & 0 \\ (3, 4, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  0 3 & 0 \end{matrix}

614

(3, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 4  1 3  −p^{2}(p − 1)^{2}

(3, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 3  2 3  p^{3}(p − 1)^{2}

(3, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  1 3  0

(3, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 3  2 3  0

(3, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  1 3  0

(3, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  0 3  0

h(3, 4, 4, 4, 3) = p^{3} − 2p^{4} + p^{5}

(3, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 4  1 4  0

(3, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  1 4  0

(3, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  1 4  0

(3, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  0 4  0

(3, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 4  1 4  −p^{3}(p − 1)

(3, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  1 4  0

(3, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  1 4  0

(3, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  0 4  0

h(3, 4, 4, 4, 4) = p^{3} − 2p^{4} + p^{5}

\begin{matrix}(3, 4, 4, 4, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  0 5 & 0 \\ (3, 4, 4, 4, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  0 5 & 0 \end{matrix} \begin{matrix}(3, 4, 4, 5, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  1 1 & 0 \\ (3, 4, 4, 5, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  1 1 & 0 \end{matrix}

617

(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 4  2 2 −p^{4}(p − 1)
(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 4  2 2  0
(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  2 2  0
(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  2 2  0
(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  1 2  0
(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 4  2 2  p^{3}(p − 1)
(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  2 2  p^{3}(p − 1)^{2}
(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  2 2  0
(3, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  1 2  0

cancel

\begin{matrix}(3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 4  2 3 & 0 \\ (3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 4  2 3 & 0 \\ (3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  2 3 & 0 \\ (3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  2 3 & 0 \\ (3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  1 3 & 0 \\ (3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 4  2 3 & 0 \\ (3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  2 3 & 0 \\ (3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  2 3 & 0 \\ (3, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  1 3 & 0 \end{matrix}

619

(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  2  1 4  2 4  p^{4}(p − 1)
(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  2  1 4  2 4  0
(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  2 4  0
(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 4  2 4  0
(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  1 4  0
(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  2  1 4  2 4  −p^{3}(p − 1)
(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  2 4 −p^{3}(p − 1)^{2}
(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 4  2 4  0
(3, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  1 4  0

cancel

\begin{matrix}(3, 4, 4, 5, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  1 5 & 0 \\ (3, 4, 4, 5, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  1 5 & 0 \end{matrix}

\begin{matrix}(3, 4, 4, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  2 2 & 0 \\ (3, 4, 4, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  2 2 & 0 \end{matrix}

(3, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  0 4  3 3  0

(3, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  2 3  0

(3, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  3 3  −p^{4}(p − 1)

(3, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  2 3  0

h(3, 4, 4, 6, 3) = p^{4} − p^{5}

(3, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  2 4  0

(3, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  0 4  3 4  −p^{4}(p − 1)

(3, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  2 4  0

h(3, 4, 4, 6, 4) = p^{4} − p^{5}

\begin{matrix}(3, 4, 4, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  0 5  2 5 & 0 \\ (3, 4, 4, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  0 5  2 5 & 0 \end{matrix}

(3, 4, 5, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  0 0  0

(3, 4, 5, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  0 0  p^{2}(p − 1)

h(3, 4, 5, 2, 0) = −p^{2} + p^{3}

(3, 4, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 2  1 1  0 ; (3, 4, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  0 1  0 ; (3, 4, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 2  1 1  p^{2}(p − 1) ; (3, 4, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  0 1  0 ; h(3, 4, 5, 2, 1) = −p^{2} + p^{3} (3, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 2  1 2  0 ; (3, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  0 2  0 ; (3, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 2  1 2  p^{2}(p − 1) ; (3, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  0 2  p^{2}(p − 1)^{2} ; h(3, 4, 5, 2, 2) = −p^{3} + p^{4}

623

(3, 4, 5, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  0 3  0 ; (3, 4, 5, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  0 3  p^{3}(p − 1) ; h(3, 4, 5, 2, 3) = −p^{3} + p^{4} \begin{matrix}(3, 4, 5, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  0 0 & 0 \\ (3, 4, 5, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  0 0 & 0 \end{matrix}

624

(3, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 3  1 1  0

(3, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 3  1 1  0

(3, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  1 1  0

(3, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  0 1  0

(3, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 3  1 1  0

(3, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 3  1 1  0

(3, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  1 1  0

(3, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  0 1  0

h(3, 4, 5, 3, 1) = −p^{3} + p^{4}

\begin{matrix}(3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  1 3  1 2 & 0 \\ (3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 3  1 2 & 0 \\ (3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 3  1 2 & 0 \\ (3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  1 2 & 0 \\ (3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  0 2 & 0 \\ (3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 3  1 2 & 0 \\ (3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 3  1 2 & 0 \\ (3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  1 2 & 0 \\ (3, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  0 2 & 0 \end{matrix}

626

(3, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 3  1 3  0

(3, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 3  1 3  0

(3, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  1 3  0

(3, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  0 3  0

(3, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 3  1 3  0

(3, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 3  1 3  0

(3, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  1 3  0

(3, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  0 3  0

h(3, 4, 5, 3, 3) = p^{3} − p^{4}

\begin{matrix}(3, 4, 5, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  0 4 & 0 \\ (3, 4, 5, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  0 4 & 0 \end{matrix} (3, 4, 5, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  0 0  0 ; (3, 4, 5, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  0 0  −p^{2}(p − 1) ; h(3, 4, 5, 4, 0) = p^{2} − p^{3}

628

(3, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  1 1  0

(3, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 4  1 1  0

(3, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  1 1  0

(3, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  0 1  0

(3, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  1 1  0

(3, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 4  1 1  p^{2}(p − 1)^{2}

(3, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  1 1  0

(3, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  0 1  0

h(3, 4, 5, 4, 1) = p^{2} − 3p^{3} + 2p^{4}

\begin{matrix}(3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  1 3  2 2 & 0 \\ (3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  1 4  1 2 & 0 \\ (3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 3  2 2 & 0 \\ (3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  1 2 & 0 \\ (3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 3  2 2 & 0 \\ (3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 4  1 2 & 0 \\ (3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  2 2 & 0 \\ (3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  1 2 & 0 \\ (3, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  0 2 & 0 \end{matrix}

630

(3, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  1 2  0

(3, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 3  2 2  p^{2}(p − 1)^{2}

(3, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 4  1 2  0

(3, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  2 2  p^{3}(p − 1)^{2}

(3, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  1 2  0

(3, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  0 2  −p^{2}(p − 1)^{2}

h(3, 4, 5, 4, 2) = p^{3} − 2p^{4} + p^{5}

\begin{matrix}(3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  1 3  2 3 & 0 \\ (3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  1 4  1 3 & p^{3}(p − 1)^{2} \\ (3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 3  2 3 & 0 \\ (3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  1 3 & 0 \\ (3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 3  2 3 & 0 \\ (3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 4  1 3 & 0 \\ (3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 3  2 3 & 0 \\ (3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  1 3 & 0 \\ (3, 4, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  0 3 & 0 \end{matrix}

632

(3, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  1 3  0

(3, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 3  2 3  p^{2}(p − 1)^{2}

(3, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 4  1 3  p^{2}(p − 1)^{3}

(3, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 3  2 3  p^{3}(p − 1)^{2}

(3, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  1 3  0

(3, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  0 3  0

h(3, 4, 5, 4, 3) = 3p^{3} − 6p^{4} + 3p^{5}

(3, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  1 4  0

(3, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 4  1 4  0

(3, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  1 4  0

(3, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  0 4  0

(3, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  1 4  0

(3, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 4  1 4  p^{3}(p − 1)^{2}

(3, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  1 4  0

(3, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  0 4  −p^{3}(p − 1)^{2}

h(3, 4, 5, 4, 4) = −p^{4} + p^{5}

(3, 4, 5, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  0 5  0 ; (3, 4, 5, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  0 5  −p^{4}(p − 1) ; h(3, 4, 5, 4, 5) = p^{4} − p^{5} (3, 4, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 5  1 1  0 ; (3, 4, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  1 1  0 ; (3, 4, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  1 1  p^{3}(p − 1) ; (3, 4, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  1 1  0 ; h(3, 4, 5, 5, 1) = −p^{3} + p^{4}

635

\begin{matrix}(3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  1 4  2 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  2 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 4  2 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 5  1 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  2 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  1 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  2 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 4  2 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  1 2 & 0 \end{matrix}

636

\begin{matrix}(3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  2 2 & 0 \\ (3, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  1 2 & 0 \end{matrix}

637

\begin{matrix}(3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  1 4  2 3 & 0 \\ (3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  2 3 & 0 \\ (3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 4  2 3 & 0 \\ (3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 5  1 3 & 0 \\ (3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  2 3 & 0 \\ (3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  1 3 & 0 \\ (3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  2 3 & 0 \\ (3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 4  2 3 & 0 \\ (3, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  1 3 & p^{3}(p − 1)^{2} \end{matrix}

638

(3, 4, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  1 3  0

h(3, 4, 5, 5, 3) = p^{3} − 2p^{4} + p^{5}

\begin{matrix}(3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  1 4  2 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  2 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 4  2 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 5  1 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  2 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  1 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  2 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 4  2 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  1 4 & 0 \end{matrix}

640

\begin{matrix}(3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  2 4 & 0 \\ (3, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  1 4 & 0 \end{matrix} (3, 4, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 5  1 5  0 ; (3, 4, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  1 5  0 ; (3, 4, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  1 5  −p^{4}(p − 1) ; (3, 4, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  1 5  0 ; h(3, 4, 5, 5, 5) = p^{4} − p^{5}

641

(3, 4, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  2 2  0

(3, 4, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  2 2  −p^{3}(p − 1)

(3, 4, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  2 2  −p^{3}(p − 1)^{2}

h(3, 4, 5, 6, 2) = p^{4} − p^{5}

(3, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  3 3  0

(3, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 5  2 3  0

(3, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  3 3  0

(3, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  2 3  0

(3, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  3 3  0

(3, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  2 3  0

(3, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  3 3  p^{4}(p − 1)^{2}

(3, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  2 3  0

h(3, 4, 5, 6, 3) = 2p^{4} − 3p^{5} + p^{6}

(3, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  1 4  3 4  0

(3, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  2  1 5  2 4  0

(3, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 4  3 4  0

(3, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  2 4  0

(3, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 4  3  1 4  3 4  0

(3, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  2 4  −p^{3}(p − 1)^{2}

(3, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 4  3 4  p^{4}(p − 1)^{2}

(3, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  2 4  −p^{3}(p − 1)^{3}

h(3, 4, 5, 6, 4) = p^{4} − p^{5}

(3, 4, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  2 5  0

(3, 4, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  2  1 5  2 5  −p^{4}(p − 1)

(3, 4, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  2 5  −p^{4}(p − 1)^{2}

h(3, 4, 5, 6, 5) = p^{5} − p^{6}

(3, 4, 5, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  3 3  0

(3, 4, 5, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  3 3  p^{5}(p − 1)

h(3, 4, 5, 7, 3) = −p^{5} + p^{6}

\begin{matrix}(3, 4, 5, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  0 5  3 4 & 0 \\ (3, 4, 5, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  3 4 & 0 \end{matrix}

(3, 4, 5, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  0 5  3 5  −p^{5}(p − 1)

h(3, 4, 5, 7, 5) = p^{5} − p^{6}

(3, 4, 6, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  0 0  −p^{3}

h(3, 4, 6, 3, 0) = −p^{3}

\begin{matrix}(3, 4, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 3  1 1 & 0 \\ (3, 4, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 3  1 1 & 0 \\ (3, 4, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  0 1 & 0 \end{matrix}

(3, 4, 6, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 3  1 2  0

(3, 4, 6, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  0 2  −p^{3}(p − 1)

h(3, 4, 6, 3, 2) = p^{3} − p^{4}

\begin{matrix}(3, 4, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 3  1 3 & 0 \\ (3, 4, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 3  1 3 & 0 \\ (3, 4, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  0 3 & 0 \end{matrix}

(3, 4, 6, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  0 4  p^{4}

h(3, 4, 6, 3, 4) = p^{4}

(3, 4, 6, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  0 0  −p^{3}

h(3, 4, 6, 4, 0) = −p^{3}

\begin{matrix}(3, 4, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 4  1 1 & 0 \\ (3, 4, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  1 1 & 0 \\ (3, 4, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  1 1 & 0 \\ (3, 4, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  0 1 & 0 \end{matrix}

648

(3, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  2 3  2 2  0

(3, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 3  2 2  0

(3, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 4  1 2  0

(3, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 3  2 2  0

(3, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  1 2  0

(3, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  1 2  0

(3, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  0 2  −p^{3}(p − 1)

h(3, 4, 6, 4, 2) = p^{3} − 2p^{4} + p^{5}

(3, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  2 3  2 3  0

(3, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 3  2 3  0

(3, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 4  1 3  0

(3, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 3  2 3  0

(3, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  1 3  0

(3, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  1 3  0

(3, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  0 3  0

h(3, 4, 6, 4, 3) = −p^{4} + p^{5}

(3, 4, 6, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  1 4  0

(3, 4, 6, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  1 4  0

(3, 4, 6, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  0 4  −p^{4}(p − 1)

h(3, 4, 6, 4, 4) = p^{4} − p^{5}

(3, 4, 6, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  0 5  −p^{5}

h(3, 4, 6, 4, 5) = −p^{5}

\begin{matrix}(3, 4, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  1 1 & 0 \\ (3, 4, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  1 1 & 0 \\ (3, 4, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  1 1 & 0 \end{matrix}

(3, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  2 4  2 2  p^{4}(p − 1)
(3, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  2 4  2 2  0
(3, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 4  2 2  0
(3, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  1 2  0
(3, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  2 2  0
(3, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  1 2  0
(3, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  2 2 −p^{4}(p − 1)
(3, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  1 2  0

cancel

\begin{matrix}(3, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  2 4  2 3 & 0 \\ (3, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  2 4  2 3 & 0 \\ (3, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 4  2 3 & 0 \\ (3, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  1 3 & 0 \\ (3, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  2 3 & 0 \\ (3, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  1 3 & 0 \\ (3, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  2 3 & 0 \\ (3, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  1 3 & 0 \end{matrix}

653

(3, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 4  3  2  1 4  3  2 4  2 4 −p^{4}(p − 1)
(3, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  2 4  2 4  0
(3, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 4  2 4  0
(3, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  1 4  0
(3, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  2 4  0
(3, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  1 4  0
(3, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  2 4  p^{4}(p − 1)
(3, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  1 4  0

cancel

\begin{matrix}(3, 4, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  1 5 & 0 \\ (3, 4, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  1 5 & 0 \\ (3, 4, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  1 5 & 0 \end{matrix} (3, 4, 6, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  2 2  0 ; (3, 4, 6, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  2 2  0 ; (3, 4, 6, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  2 2  −p^{4}(p − 1) ; h(3, 4, 6, 6, 2) = p^{4} − p^{5}

655

(3, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  2 4  3 3  0

(3, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 4  3 3  0

(3, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  2 3  0

(3, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  3 3  0

(3, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  2 3  0

(3, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  3 3  0

(3, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  2 3  0

h(3, 4, 6, 6, 3) = p^{4} − p^{5}

(3, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 4  3  2 4  3 4  0

(3, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 4  3 4  0

(3, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  2 4  0

(3, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 4  3 4  0

(3, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  2 4  0

(3, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 4  3 4  0

(3, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  2 4  −p^{4}(p − 1)^{2}

h(3, 4, 6, 6, 4) = p^{5} − p^{6}

(3, 4, 6, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  2 5  0

(3, 4, 6, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  2 5  −p^{5}(p − 1)

h(3, 4, 6, 6, 5) = p^{5} − p^{6}

\begin{matrix}(3, 4, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  3 3 & 0 \\ (3, 4, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  3 3 & 0 \\ (3, 4, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  3 3 & 0 \end{matrix}

\begin{matrix}(3, 4, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  3 4 & 0 \\ (3, 4, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  3 4 & 0 \\ (3, 4, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  3 4 & 0 \end{matrix}

\begin{matrix}(3, 4, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  1 5  3 5 & 0 \\ (3, 4, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  3  1 5  3 5 & 0 \\ (3, 4, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  3 5 & 0 \end{matrix}

(3, 4, 6, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  4 4  p^{6}

h(3, 4, 6, 8, 4) = p^{6}

(3, 4, 6, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  0 5  4 5  p^{6}

h(3, 4, 6, 8, 5) = p^{6}

(3, 4, 7, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  1 1  −p^{4}

h(3, 4, 7, 4, 1) = −p^{4}

\begin{matrix}(3, 4, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 3  2 2 & 0 \\ (3, 4, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  1 2 & 0 \end{matrix}

(3, 4, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  1 3  −p^{4}(p − 1)

h(3, 4, 7, 4, 3) = p^{4} − p^{5}

(3, 4, 7, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  1 4  −p^{5}

h(3, 4, 7, 4, 4) = −p^{5}

(3, 4, 7, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  1 1  −p^{4}

h(3, 4, 7, 5, 1) = −p^{4}

\begin{matrix}(3, 4, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 4  2 2 & 0 \\ (3, 4, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  2 2 & 0 \\ (3, 4, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  1 2 & 0 \end{matrix}

(3, 4, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  2 3  0

(3, 4, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  1 3  −p^{4}(p − 1)

h(3, 4, 7, 5, 3) = p^{4} − p^{5}

\begin{matrix}(3, 4, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 4  2 4 & 0 \\ (3, 4, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  2 4 & 0 \\ (3, 4, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  1 4 & 0 \end{matrix}

(3, 4, 7, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  1 5  p^{5}

h(3, 4, 7, 5, 5) = p^{5}

\begin{matrix}(3, 4, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 5  2 2 & 0 \\ (3, 4, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  2 2 & 0 \end{matrix} (3, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 4  3 3  0 ; (3, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 5  2 3  0 ; (3, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  3 3  −p^{5}(p − 1) ; (3, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  2 3  0 ; h(3, 4, 7, 6, 3) = p^{5} − p^{6}

662

(3, 4, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 5  2 4  0

(3, 4, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 4  3 4  −p^{5}(p − 1)

(3, 4, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  2 4  0

h(3, 4, 7, 6, 4) = p^{5} − p^{6}

\begin{matrix}(3, 4, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 5  2 5 & 0 \\ (3, 4, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  2 5 & 0 \end{matrix}

(3, 4, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 5  3 3  0

(3, 4, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  3 3  −p^{5}(p − 1)

h(3, 4, 7, 7, 3) = p^{5} − p^{6}

\begin{matrix}(3, 4, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 5  3 4 & 0 \\ (3, 4, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  3 4 & 0 \end{matrix}

(3, 4, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  0 5  3  2 5  3 5  0

(3, 4, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  3 5  p^{5}(p − 1)

h(3, 4, 7, 7, 5) = −p^{5} + p^{6}

(3, 4, 7, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  4 4  p^{6}

h(3, 4, 7, 8, 4) = p^{6}

(3, 4, 7, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  1  0 5  4  1 5  4 5  p^{6}

h(3, 4, 7, 8, 5) = p^{6}

(3, 5, 3, 1, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 2  0 0 0

(3, 5, 3, 1, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 2  0 1 0

(3, 5, 3, 1, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 2  0 2 0

(3, 5, 3, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  0 0 0

(3, 5, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 3  2  1 2  1 1  −p^{3}(p − 1)

(3, 5, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 2  1 1  0

(3, 5, 3, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  0 1  0

h(3, 5, 3, 2, 1) = p^{3} − p^{4}

(3, 5, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 3  2  1 2  1 2  −p^{3}(p − 1)

(3, 5, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 2  1 2  0

(3, 5, 3, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  0 2  0

h(3, 5, 3, 2, 2) = p^{3} − p^{4}

(3, 5, 3, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  0 3 0

(3, 5, 3, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  0 0 0

(3, 5, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 3  2  1 3  1 1  −p^{3}(p − 1)

(3, 5, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  1 1  0

(3, 5, 3, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  0 1  0

h(3, 5, 3, 3, 1) = p^{3} − p^{4}

\begin{matrix}(3, 5, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 3  2  1 3  1 2 & 0 \\ (3, 5, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  1 2 & 0 \\ (3, 5, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  0 2 & 0 \end{matrix}

(3, 5, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  1 3  0

(3, 5, 3, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  0 3  0

h(3, 5, 3, 3, 3) = −p^{3} + p^{4}

(3, 5, 3, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  0 4 0

(3, 5, 3, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  1 1 0

(3, 5, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 3  2  1 3  2 2  p^{3}(p − 1)

(3, 5, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  2 2  0

(3, 5, 3, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  1 2  0

h(3, 5, 3, 4, 2) = −p^{3} + p^{4}

(3, 5, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 3  2 3  0

(3, 5, 3, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  1 3  0

h(3, 5, 3, 4, 3) = −p^{3} + p^{4}

(3, 5, 3, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  1 4 0

(3, 5, 3, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  2 2 0

(3, 5, 3, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  2 3 0

(3, 5, 3, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  0 4  2 4 0

(3, 5, 4, 1, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 2  0 0 0

(3, 5, 4, 1, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 2  0 1 0

(3, 5, 4, 1, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 2  0 2 0

\begin{matrix}(3, 5, 4, 2, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  0 0 & 0 \\ (3, 5, 4, 2, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  0 0 & 0 \end{matrix}

\begin{matrix}(3, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 2  1 1 & 0 \\ (3, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 2  1 1 & 0 \\ (3, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  0 1 & 0 \\ (3, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 2  1 1 & 0 \\ (3, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(3, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 2  1 2 & 0 \\ (3, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 2  1 2 & 0 \\ (3, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  0 2 & 0 \\ (3, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 2  1 2 & 0 \\ (3, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  0 2 & 0 \end{matrix}

\begin{matrix}(3, 5, 4, 2, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  0 3 & 0 \\ (3, 5, 4, 2, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  0 3 & 0 \end{matrix}

\begin{matrix}(3, 5, 4, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  0 0 & 0 \\ (3, 5, 4, 3, 0) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  0 0 & 0 \end{matrix}

\begin{matrix}(3, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 3  1 1 & 0 \\ (3, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 3  1 1 & 0 \\ (3, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  1 1 & 0 \\ (3, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  0 1 & 0 \\ (3, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  1 1 & 0 \\ (3, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  0 1 & 0 \end{matrix}

671

\begin{matrix}(3, 5, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 3  1 2 & 0 \\ (3, 5, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 3  1 2 & 0 \\ (3, 5, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  1 2 & 0 \\ (3, 5, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  0 2 & 0 \\ (3, 5, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  1 2 & 0 \\ (3, 5, 4, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  0 2 & 0 \end{matrix}

672

\begin{matrix}(3, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 3  1 3 & 0 \\ (3, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 3  1 3 & 0 \\ (3, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  1 3 & 0 \\ (3, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  0 3 & 0 \\ (3, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  1 3 & 0 \\ (3, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  0 3 & 0 \end{matrix}

\begin{matrix}(3, 5, 4, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  0 4 & 0 \\ (3, 5, 4, 3, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  0 4 & 0 \end{matrix}

(3, 5, 4, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  0 0 0

\begin{matrix}(3, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 4  1 1 & 0 \\ (3, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 4  1 1 & 0 \\ (3, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  1 1 & 0 \\ (3, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  1 1 & 0 \\ (3, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  0 1 & 0 \end{matrix}

674

\begin{matrix}(3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 3  2 2 & 0 \\ (3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 4  1 2 & 0 \\ (3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 3  2 2 & 0 \\ (3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 4  1 2 & 0 \\ (3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  2 2 & 0 \\ (3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  1 2 & 0 \\ (3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  2 2 & 0 \\ (3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  1 2 & 0 \\ (3, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  0 2 & 0 \end{matrix}

675

\begin{matrix}(3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 3  2 3 & 0 \\ (3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 4  1 3 & 0 \\ (3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 3  2 3 & 0 \\ (3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 4  1 3 & 0 \\ (3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 3  2 3 & 0 \\ (3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  1 3 & 0 \\ (3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 3  2 3 & 0 \\ (3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  1 3 & 0 \\ (3, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  0 3 & 0 \end{matrix}

676

\begin{matrix}(3, 5, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 4  1 4 & 0 \\ (3, 5, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 4  1 4 & 0 \\ (3, 5, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  1 4 & 0 \\ (3, 5, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  1 4 & 0 \\ (3, 5, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  0 4 & 0 \end{matrix}

(3, 5, 4, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  0 5 0

(3, 5, 4, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  1 1 0

\begin{matrix}(3, 5, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 4  2 2 & 0 \\ (3, 5, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 4  2 2 & 0 \\ (3, 5, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  2 2 & 0 \\ (3, 5, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  2 2 & 0 \\ (3, 5, 4, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  1 2 & 0 \end{matrix}

678

\begin{matrix}(3, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 4  2 3 & 0 \\ (3, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 4  2 3 & 0 \\ (3, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  2 3 & 0 \\ (3, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  2 3 & 0 \\ (3, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  1 3 & 0 \end{matrix}

679

\begin{matrix}(3, 5, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  2  1 4  2 4 & 0 \\ (3, 5, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  2  1 4  2 4 & 0 \\ (3, 5, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  2 4 & 0 \\ (3, 5, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 4  2 4 & 0 \\ (3, 5, 4, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  1 4 & 0 \end{matrix}

(3, 5, 4, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  1 5 0

(3, 5, 4, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  2 2 0

\begin{matrix}(3, 5, 4, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  3 3 & 0 \\ (3, 5, 4, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  2 3 & 0 \end{matrix}

\begin{matrix}(3, 5, 4, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  0 4  3 4 & 0 \\ (3, 5, 4, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  2 4 & 0 \end{matrix}

(3, 5, 4, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  0 5  2 5 0

(3, 5, 5, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  0 0 0

(3, 5, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 2  1 1  p^{3}(p − 1)

(3, 5, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 2  1 1  0

(3, 5, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  0 1  0

h(3, 5, 5, 2, 1) = −p^{3} + p^{4}

(3, 5, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 2  1 2  0

(3, 5, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  0 2  0

h(3, 5, 5, 2, 2) = −p^{3} + p^{4}

(3, 5, 5, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  0 3 0

(3, 5, 5, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  0 0 0

(3, 5, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 3  1 1  0

(3, 5, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 3  1 1  0

(3, 5, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 3  1 1  0

(3, 5, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  1 1  0

(3, 5, 5, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  0 1  0

h(3, 5, 5, 3, 1) = −p^{3} + 2p^{4} − p^{5}

\begin{matrix}(3, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 3  1 2 & 0 \\ (3, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 3  1 2 & 0 \\ (3, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 3  1 2 & 0 \\ (3, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 3  1 2 & 0 \\ (3, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  1 2 & 0 \\ (3, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  0 2 & 0 \end{matrix}

684

(3, 5, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 3  1 3  0

(3, 5, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 3  1 3  0

(3, 5, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 3  1 3  0

(3, 5, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  1 3  0

(3, 5, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  0 3  0

h(3, 5, 5, 3, 3) = p^{3} − 2p^{4} + p^{5}

(3, 5, 5, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  0 4 0

(3, 5, 5, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  0 0 0

(3, 5, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 4  1 1 −p^{3}(p − 1)^{2}
(3, 5, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 4  1 1  p^{3}(p − 1)^{2}
(3, 5, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  1 1  0
(3, 5, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 4  1 1  0
(3, 5, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  1 1  0
(3, 5, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  0 1  0

cancel

\begin{matrix}(3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 3  2 2 & 0 \\ (3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 4  1 2 & 0 \\ (3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 3  2 2 & p^{3}(p − 1)^{2} \\ (3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 4  1 2 & 0 \\ (3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 3  2 2 & 0 \\ (3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  1 2 & 0 \\ (3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 3  2 2 & 0 \\ (3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 4  1 2 & 0 \\ (3, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  2 2 & 0 \end{matrix}

687

(3, 5, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  0 2  0

h(3, 5, 5, 4, 2) = p^{3} − 2p^{4} + p^{5}

\begin{matrix}(3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 3  2 3 & 0 \\ (3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 4  1 3 & −p^{3}(p − 1)^{3} \\ (3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 3  2 3 & p^{3}(p − 1)^{2} \\ (3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 4  1 3 & p^{3}(p − 1)^{3} \\ (3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 3  2 3 & 0 \\ (3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  1 3 & 0 \\ (3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 3  2 3 & 0 \\ (3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 4  1 3 & 0 \\ (3, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 3  2 3 & 0 \end{matrix}

689

(3, 5, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  1 3  0 ; (3, 5, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  0 3  0 ; h(3, 5, 5, 4, 3) = p^{3} − 2p^{4} + p^{5} (3, 5, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 4  1 4 −p^{4}(p − 1)^{2} ; (3, 5, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 4  1 4  p^{4}(p − 1)^{2} ; (3, 5, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  1 4  0 ; (3, 5, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 4  1 4  0 ; (3, 5, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  1 4  0 ; (3, 5, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  0 4  0 ; cancel

690

(3, 5, 5, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  0 5 0 (3, 5, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  1 1  p^{4}(p − 1) ; (3, 5, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  1 1  0 ; (3, 5, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  1 1  0 ; h(3, 5, 5, 5, 1) = −p^{4} + p^{5}

691

\begin{matrix}(3, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 4  2 2 & 0 \\ (3, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 4  2 2 & 0 \\ (3, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  1 2 & 0 \\ (3, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  2 2 & 0 \\ (3, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 4  2 2 & 0 \\ (3, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  1 2 & 0 \\ (3, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  2 2 & 0 \\ (3, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  1 2 & 0 \end{matrix}

692

(3, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 4  2 3  0

(3, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  1 3  p^{4}(p − 1)^{2}

(3, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  2 3  0

(3, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 4  2 3  0

(3, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  1 3  0

(3, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  2 3  0

(3, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  1 3  0

h(3, 5, 5, 5, 3) = p^{4} − 2p^{5} + p^{6}

\begin{matrix}(3, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 4  2 4 & 0 \\ (3, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 4  2 4 & 0 \\ (3, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  1 4 & 0 \\ (3, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  2 4 & 0 \\ (3, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 4  2 4 & 0 \\ (3, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  1 4 & 0 \\ (3, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  2 4 & 0 \\ (3, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  1 4 & 0 \end{matrix}

694

(3, 5, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  1 5  −p^{5}(p − 1) ; (3, 5, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  1 5  0 ; (3, 5, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  1 5  0 ; h(3, 5, 5, 5, 5) = p^{5} − p^{6} (3, 5, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  2 2  −p^{4}(p − 1) ; (3, 5, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  2 2  0 ; (3, 5, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  2 2  0 ; h(3, 5, 5, 6, 2) = p^{4} − p^{5}

695

(3, 5, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  2 3  0

(3, 5, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  3 3  0

(3, 5, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  2 3  0

(3, 5, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  3 3  0

(3, 5, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  2 3  0

h(3, 5, 5, 6, 3) = p^{4} − 2p^{5} + p^{6}

(3, 5, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  1 4  3 4  p^{4}(p − 1)^{2} ; (3, 5, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  2 4 −p^{4}(p − 1)^{2} ; (3, 5, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  1 4  3 4  0 ; (3, 5, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  2 4  0 ; (3, 5, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 4  3 4  0 ; (3, 5, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  2 4  0 ; cancel (3, 5, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  2  1 5  2 5  −p^{5}(p − 1) ; (3, 5, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  2  1 5  2 5  0 ; (3, 5, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  2 5  0 ; h(3, 5, 5, 6, 5) = p^{5} − p^{6}

697

(3, 5, 5, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  3 3 0

(3, 5, 5, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  3 4 0

(3, 5, 5, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  0 5  3 5 0

(3, 5, 6, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  0 0 0

(3, 5, 6, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 3  1 1  −p^{4}(p − 1)

(3, 5, 6, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 3  1 1  0

(3, 5, 6, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  0 1  0

h(3, 5, 6, 3, 1) = p^{4} − p^{5}

\begin{matrix}(3, 5, 6, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 3  1 2 & 0 \\ (3, 5, 6, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 3  1 2 & 0 \\ (3, 5, 6, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  0 2 & 0 \end{matrix}

(3, 5, 6, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 3  1 3  p^{4}(p − 1)

(3, 5, 6, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 3  1 3  0

(3, 5, 6, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  0 3  0

h(3, 5, 6, 3, 3) = −p^{4} + p^{5}

(3, 5, 6, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  0 4 0

(3, 5, 6, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  0 0 0

\begin{matrix}(3, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  1 1 & 0 \\ (3, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  1 1 & 0 \\ (3, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  1 1 & 0 \\ (3, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  0 1 & 0 \end{matrix}

700

\begin{matrix}(3, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  2 3  2 2 & 0 \\ (3, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 3  2 2 & 0 \\ (3, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  1 2 & 0 \\ (3, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  2 3  2 2 & 0 \\ (3, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 3  2 2 & 0 \\ (3, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  1 2 & 0 \\ (3, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  1 2 & 0 \\ (3, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  0 2 & 0 \end{matrix}

701

\begin{matrix}(3, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  2 3  2 3 & 0 \\ (3, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 3  2 3 & 0 \\ (3, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  1 3 & 0 \\ (3, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  2 3  2 3 & 0 \\ (3, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 3  2 3 & 0 \\ (3, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  1 3 & 0 \\ (3, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  1 3 & 0 \\ (3, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  0 3 & 0 \end{matrix}

702

\begin{matrix}(3, 5, 6, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  1 4 & 0 \\ (3, 5, 6, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  1 4 & 0 \\ (3, 5, 6, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  1 4 & 0 \\ (3, 5, 6, 4, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  0 4 & 0 \end{matrix}

(3, 5, 6, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  0 5 0

(3, 5, 6, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  1 1  p^{4}(p − 1)

(3, 5, 6, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  1 1  0

(3, 5, 6, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  1 1  0

h(3, 5, 6, 5, 1) = −p^{4} + p^{5}

\begin{matrix}(3, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  2 4  2 2 & 0 \\ (3, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  2 2 & 0 \\ (3, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  1 2 & 0 \\ (3, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  2 4  2 2 & 0 \\ (3, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  2 2 & 0 \\ (3, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  1 2 & 0 \\ (3, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  2 2 & 0 \\ (3, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  1 2 & 0 \end{matrix}

704

(3, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  2 3  0

(3, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  1 3  p^{4}(p − 1)^{2}

(3, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  2 4  2 3  0

(3, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  2 3  0

(3, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  1 3  0

(3, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  2 3  0

(3, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  1 3  0

h(3, 5, 6, 5, 3) = p^{4} − 2p^{5} + p^{6}

\begin{matrix}(3, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  2 4  2 4 & 0 \\ (3, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  2 4 & 0 \\ (3, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  1 4 & 0 \\ (3, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  2 4  2 4 & 0 \\ (3, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  2 4 & 0 \\ (3, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  1 4 & 0 \\ (3, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  2 4 & 0 \\ (3, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  1 4 & 0 \end{matrix}

706

(3, 5, 6, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  1 5  −p^{5}(p − 1) ; (3, 5, 6, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  1 5  0 ; (3, 5, 6, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  1 5  0 ; h(3, 5, 6, 5, 5) = p^{5} − p^{6} \begin{matrix}(3, 5, 6, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  2 2 & 0 \\ (3, 5, 6, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  2 2 & 0 \\ (3, 5, 6, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  2 2 & 0 \end{matrix}

707

\begin{matrix}(3, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  2 4  3 3 & 0 \\ (3, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  3 3 & 0 \\ (3, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  2 3 & 0 \\ (3, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  2 4  3 3 & 0 \\ (3, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  3 3 & 0 \\ (3, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  2 3 & 0 \\ (3, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  3 3 & 0 \\ (3, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  2 3 & 0 \end{matrix}

708

\begin{matrix}(3, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 4  3  2 4  3 4 & 0 \\ (3, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 4  3 4 & 0 \\ (3, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  2 4 & 0 \\ (3, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 4  3  2 4  3 4 & 0 \\ (3, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 4  3 4 & 0 \\ (3, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  2 4 & 0 \\ (3, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 4  3 4 & 0 \\ (3, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  2 4 & 0 \end{matrix}

709

\begin{matrix}(3, 5, 6, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  2 5 & 0 \\ (3, 5, 6, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  2 5 & 0 \\ (3, 5, 6, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  2 5 & 0 \end{matrix}

(3, 5, 6, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  3 3  −p^{5}(p − 1)

(3, 5, 6, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  3 3  0

(3, 5, 6, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  3 3  0

h(3, 5, 6, 7, 3) = p^{5} − p^{6}

\begin{matrix}(3, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  1 5  3 4 & 0 \\ (3, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  3 4 & 0 \\ (3, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  3 4 & 0 \end{matrix}

(3, 5, 6, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  1 5  3 5  0

(3, 5, 6, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  3 5  0

h(3, 5, 6, 7, 5) = −p^{5} + p^{6}

(3, 5, 6, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  4 4 0

(3, 5, 6, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  0 5  4 5 0

(3, 5, 7, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  1 1 0

(3, 5, 7, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 3  2 2  0

(3, 5, 7, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  1 2  0

h(3, 5, 7, 4, 2) = p^{4} − p^{5}

(3, 5, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 3  2 3  −p^{4}(p − 1)

(3, 5, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 3  2 3  0

(3, 5, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  1 3  0

h(3, 5, 7, 4, 3) = p^{4} − p^{5}

(3, 5, 7, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  1 4 0

(3, 5, 7, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  1 1 0

\begin{matrix}(3, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 4  2 2 & 0 \\ (3, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 4  2 2 & 0 \\ (3, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  2 2 & 0 \\ (3, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  1 2 & 0 \end{matrix} \begin{matrix}(3, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 4  2 3 & 0 \\ (3, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 4  2 3 & 0 \\ (3, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  2 3 & 0 \\ (3, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  1 3 & 0 \end{matrix}

713

\begin{matrix}(3, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 4  2 4 & 0 \\ (3, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 4  2 4 & 0 \\ (3, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  2 4 & 0 \\ (3, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  1 4 & 0 \end{matrix}

(3, 5, 7, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  1 5 0

(3, 5, 7, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 5  2 2  p^{4}(p − 1)

(3, 5, 7, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 5  2 2  0

(3, 5, 7, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  2 2  0

h(3, 5, 7, 6, 2) = −p^{4} + p^{5}

(3, 5, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 5  2 3  0

(3, 5, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 4  3 3  0

(3, 5, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 5  2 3  0

(3, 5, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  3 3  0

(3, 5, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  2 3  0

h(3, 5, 7, 6, 3) = −p^{4} + 2p^{5} − p^{6}

(3, 5, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 4  3 4 −p^{4}(p − 1)^{2} ; (3, 5, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 5  2 4  p^{4}(p − 1)^{2} ; (3, 5, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 4  3 4  0 ; (3, 5, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 5  2 4  0 ; (3, 5, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 4  3 4  0 ; (3, 5, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  2 4  0 ; cancel (3, 5, 7, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 5  2 5  p^{5}(p − 1) ; (3, 5, 7, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 5  2 5  0 ; (3, 5, 7, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  2 5  0 ; h(3, 5, 7, 6, 5) = −p^{5} + p^{6}

716

(3, 5, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 5  3 3  −p^{5}(p − 1) ; (3, 5, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 5  3 3  0 ; (3, 5, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  3 3  0 ; h(3, 5, 7, 7, 3) = p^{5} − p^{6} \begin{matrix}(3, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  3  2  1 5  3  2 5  3 4 & 0 \\ (3, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 5  3 4 & 0 \\ (3, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  3 4 & 0 \end{matrix}

717

(3, 5, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  3  2 5  3 5  0

(3, 5, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  3 5  0

h(3, 5, 7, 7, 5) = −p^{5} + p^{6}

(3, 5, 7, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  4 4 0

(3, 5, 7, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  1 5  4 5 0

(3, 5, 8, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 4  2 2 0

(3, 5, 8, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 4  2 3 0

(3, 5, 8, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 4  2 4 0

(3, 5, 8, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  2 2 0

\begin{matrix}(3, 5, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 4  3 3 & 0 \\ (3, 5, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  2 3 & 0 \end{matrix}

\begin{matrix}(3, 5, 8, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 4  3 4 & 0 \\ (3, 5, 8, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  2 4 & 0 \end{matrix}

(3, 5, 8, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  2 5 0

(3, 5, 8, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  3 3 0

(3, 5, 8, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  3 4 0

(3, 5, 8, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  3 5 0

(3, 5, 8, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  4 4 0

(3, 5, 8, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  0 5  4  2 5  4 5 0

(3, 6, 4, 2, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  0 0  −p^{3}

h(3, 6, 4, 2, 0) = −p^{3}

(3, 6, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 2  1 1  p^{3}(p − 1)

(3, 6, 4, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  0 1  0

h(3, 6, 4, 2, 1) = −p^{3} + p^{4}

(3, 6, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 2  1 2  p^{3}(p − 1)

(3, 6, 4, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  0 2 −p^{3}(p − 1)

cancel

(3, 6, 4, 2, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  0 3  −p^{4}

h(3, 6, 4, 2, 3) = −p^{4}

h(3, 6, 4, 3, 0) = −p^{3}

\begin{matrix}(3, 6, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 3  1 1 & 0 \\ (3, 6, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  1 1 & 0 \\ (3, 6, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  0 1 & 0 \end{matrix}

(3, 6, 4, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 3  1 2  0

(3, 6, 4, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  1 2  0

(3, 6, 4, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  0 2  −p^{3}(p − 1)

h(3, 6, 4, 3, 2) = p^{3} − p^{4}

\begin{matrix}(3, 6, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 3  1 3 & 0 \\ (3, 6, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  1 3 & 0 \\ (3, 6, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  0 3 & 0 \end{matrix}

(3, 6, 4, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  0 4  p^{4}

h(3, 6, 4, 3, 4) = p^{4}

(3, 6, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 4  1 1  −p^{3}(p − 1)

(3, 6, 4, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  1 1  0

h(3, 6, 4, 4, 1) = p^{3} − p^{4}

(3, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 3  2 2  p^{3}(p − 1)^{2} ; (3, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 4  1 2  0 ; (3, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  2 2  −p^{4}(p − 1) ; (3, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  1 2  0 ; h(3, 6, 4, 4, 2) = p^{3} − p^{4} (3, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 3  2 3  p^{3}(p − 1)^{2} ; (3, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 4  1 3  −p^{3}(p − 1)^{2} ; (3, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 3  2 3  −p^{4}(p − 1) ; (3, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  1 3  0 ; h(3, 6, 4, 4, 3) = p^{4} − p^{5}

723

(3, 6, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 4  1 4  −p^{4}(p − 1)
(3, 6, 4, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  1 4  0

h(3, 6, 4, 4, 4) = p^{4} − p^{5}

(3, 6, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 4  2 2  p^{4}(p − 1)
(3, 6, 4, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  2 2 −p^{4}(p − 1)

cancel

\begin{matrix}(3, 6, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 4  2 3 & 0 \\ (3, 6, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  2 3 & 0 \end{matrix}
(3, 6, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  2  1 4  2 4 −p^{4}(p − 1)
(3, 6, 4, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  2 4  p^{4}(p − 1)

cancel

(3, 6, 4, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  0 4  3 3  p^{5}

h(3, 6, 4, 6, 3) = p^{5}

(3, 6, 4, 6, 4) 5 4 3 2 1 0 5 4 3 1 0 5 4 3 0 4 3 0 4 3 4 p^{5}

h(3, 6, 4, 6, 4) = p^{5}

(3, 6, 5, 2, 0) 5 4 3 2 1 0 5 4 3 1 0 5 4 3 0 5 3 0 3 0 0 −p^{3}

h(3, 6, 5, 2, 0) = −p^{3}

(3, 6, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 2  1 1  p^{3}(p − 1)
(3, 6, 5, 2, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 3  0 1  0

h(3, 6, 5, 2, 1) = −p^{3} + p^{4}

(3, 6, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 2  1 2  p^{3}(p − 1)
(3, 6, 5, 2, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 3  0 2 −p^{3}(p − 1)

cancel

h(3, 6, 5, 2, 3) = −p^{4}

(3, 6, 5, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  0 0 0

\begin{matrix}(3, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 3  1 1 & 0 \\ (3, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 3  1 1 & 0 \\ (3, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 3  1 1 & 0 \\ (3, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 3  1 1 & 0 \\ (3, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  0 1 & 0 \end{matrix}

\begin{matrix}(3, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 3  1 2 & 0 \\ (3, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 3  1 2 & 0 \\ (3, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 3  1 2 & 0 \\ (3, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 3  1 2 & 0 \\ (3, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  0 2 & 0 \end{matrix}

727

\begin{matrix}(3, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 3  1 3 & 0 \\ (3, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 3  1 3 & 0 \\ (3, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 3  1 3 & 0 \\ (3, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 3  1 3 & 0 \\ (3, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  0 3 & 0 \end{matrix}

(3, 6, 5, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  0 4 0

(3, 6, 5, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  0 0  p^{3}

h(3, 6, 5, 4, 0) = p^{3}

(3, 6, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 4  1 1  p^{3}(p − 1)^{2}

(3, 6, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  1 1  0

(3, 6, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  1 1  0

(3, 6, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  0 1  0

h(3, 6, 5, 4, 1) = p^{3} − 2p^{4} + p^{5}

(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 3  2 2  0
(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 4  1 2  0
(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 3  2 2  p^{3}(p − 1)^{2}
(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 4  1 2  0
(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 3  2 2  0
(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  1 2  0
(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 3  2 2 −p^{4}(p − 1)
(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  1 2  0
(3, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  0 2  p^{3}(p − 1)

cancel

(3, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 4  1 3  0

(3, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 3  2 3  p^{3}(p − 1)^{2}

(3, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 4  1 3  p^{3}(p − 1)^{3}

(3, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 3  2 3  0

(3, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  1 3  0

(3, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 3  2 3  −p^{4}(p − 1)

(3, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  1 3  0

(3, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  0 3  0

h(3, 6, 5, 4, 3) = 2p^{4} − 3p^{5} + p^{6}

(3, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 4  1 4  p^{4}(p − 1)^{2}

(3, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  1 4  0

(3, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  1 4  0

(3, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  0 4  p^{4}(p − 1)

h(3, 6, 5, 4, 4) = −p^{5} + p^{6}

(3, 6, 5, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  0 5  p^{5}

h(3, 6, 5, 4, 5) = p^{5}

(3, 6, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  1 1  p^{4}(p − 1)

(3, 6, 5, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  1 1  0

h(3, 6, 5, 5, 1) = −p^{4} + p^{5}

\begin{matrix}(3, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 4  2 2 & 0 \\ (3, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 4  2 2 & 0 \\ (3, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  1 2 & 0 \\ (3, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  2 2 & 0 \\ (3, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  2 2 & 0 \\ (3, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  1 2 & 0 \end{matrix}

733

(3, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 4  2 3  0

(3, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  1 3  p^{4}(p − 1)^{2}

(3, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  2 3  0

(3, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  2 3  0

(3, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  1 3  0

h(3, 6, 5, 5, 3) = p^{4} − 2p^{5} + p^{6}

\begin{matrix}(3, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 4  2 4 & 0 \\ (3, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 4  2 4 & 0 \\ (3, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  1 4 & 0 \\ (3, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  2 4 & 0 \\ (3, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  2 4 & 0 \\ (3, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  1 4 & 0 \end{matrix} (3, 6, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  1 5  −p^{5}(p − 1) ; (3, 6, 5, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  1 5  0 ; h(3, 6, 5, 5, 5) = p^{5} − p^{6}

735

(3, 6, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  2 2 −p^{4}(p − 1) ; (3, 6, 5, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  2 2  p^{4}(p − 1) ; cancel (3, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  1 4  3 3  0 ; (3, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  2 3  0 ; (3, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  3 3  0 ; (3, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  3 3  −p^{5}(p − 1) ; (3, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  2 3  0 ; h(3, 6, 5, 6, 3) = p^{5} − p^{6}

736

(3, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  2 4  −p^{4}(p − 1)^{2}

(3, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  1 4  3 4  0

(3, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 4  3 4  −p^{5}(p − 1)

(3, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  2 4  p^{4}(p − 1)^{2}

h(3, 6, 5, 6, 4) = p^{5} − p^{6}

(3, 6, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  2  1 5  2 5 −p^{5}(p − 1)

(3, 6, 5, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  2 5  p^{5}(p − 1)

cancel

(3, 6, 5, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  3 3  −p^{6}

h(3, 6, 5, 7, 3) = −p^{6}

(3, 6, 5, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  3 4 0

(3, 6, 5, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  0 5  3 5  p^{6}

h(3, 6, 5, 7, 5) = p^{6}

(3, 6, 6, 3, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  0 0  p^{3}

h(3, 6, 6, 3, 0) = p^{3}

\begin{matrix}(3, 6, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 3  1 1 & 0 \\ (3, 6, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 3  1 1 & 0 \\ (3, 6, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  0 1 & 0 \end{matrix}

(3, 6, 6, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 3  1 2  0

(3, 6, 6, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  0 2  p^{3}(p − 1)

h(3, 6, 6, 3, 2) = −p^{3} + p^{4}

\begin{matrix}(3, 6, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 3  1 3 & 0 \\ (3, 6, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 3  1 3 & 0 \\ (3, 6, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  0 3 & 0 \end{matrix}

(3, 6, 6, 3, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  0 4  −p^{4}

h(3, 6, 6, 3, 4) = −p^{4}

(3, 6, 6, 4, 0) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  0 0  p^{3}

h(3, 6, 6, 4, 0) = p^{3}

\begin{matrix}(3, 6, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 4  1 1 & 0 \\ (3, 6, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  1 1 & 0 \\ (3, 6, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  1 1 & 0 \\ (3, 6, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  0 1 & 0 \end{matrix}

740

(3, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 3  2 2  0

(3, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 4  1 2  0

(3, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  2 3  2 2  −p^{5}(p − 1)

(3, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 3  2 2  0

(3, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  1 2  0

(3, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  1 2  0

(3, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  0 2  p^{3}(p − 1)

h(3, 6, 6, 4, 2) = −p^{3} + 2p^{4} − p^{5}

(3, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 3  2 3  0

(3, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 4  1 3  0

(3, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  2 3  2 3  −p^{5}(p − 1)

(3, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 3  2 3  0

(3, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  1 3  0

(3, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  1 3  0

(3, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  0 3  0

h(3, 6, 6, 4, 3) = p^{4} − p^{5}

(3, 6, 6, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  1 4  0

(3, 6, 6, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  1 4  0

(3, 6, 6, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  0 4  p^{4}(p − 1)

h(3, 6, 6, 4, 4) = −p^{4} + p^{5}

(3, 6, 6, 4, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  0 5  p^{5}

h(3, 6, 6, 4, 5) = p^{5}

\begin{matrix}(3, 6, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  1 1 & 0 \\ (3, 6, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  1 1 & 0 \\ (3, 6, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  1 1 & 0 \end{matrix}

(3, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  2 4  2 2  p^{4}(p − 1)^{2}
(3, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 4  2 2  0
(3, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  1 2  0
(3, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  2 4  2 2 −p^{5}(p − 1)
(3, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  2 2  0
(3, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  1 2  0
(3, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  2 2  p^{4}(p − 1)
(3, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  1 2  0

cancel

\begin{matrix}(3, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  2 4  2 3 & 0 \\ (3, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 4  2 3 & 0 \\ (3, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  1 3 & 0 \\ (3, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  2 4  2 3 & 0 \\ (3, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  2 3 & 0 \\ (3, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  1 3 & 0 \\ (3, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  2 3 & 0 \\ (3, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  1 3 & 0 \end{matrix}

745

(3, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 4  3  2 4  2 4 −p^{4}(p − 1)^{2}
(3, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 4  2 4  0
(3, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  1 4  0
(3, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  2 4  2 4  p^{5}(p − 1)
(3, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  2 4  0
(3, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  1 4  0
(3, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  2 4  −p^{4}(p − 1)
(3, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  1 4  0

cancel

\begin{matrix}(3, 6, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  1 5 & 0 \\ (3, 6, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  1 5 & 0 \\ (3, 6, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  1 5 & 0 \end{matrix} (3, 6, 6, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  2 2  0 ; (3, 6, 6, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  2 2  0 ; (3, 6, 6, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  2 2  p^{4}(p − 1) ; h(3, 6, 6, 6, 2) = −p^{4} + p^{5}

747

(3, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 4  3 3  0

(3, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  2 3  0

(3, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  2 4  3 3  p^{5}(p − 1)

(3, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  3 3  0

(3, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  2 3  0

(3, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  3 3  0

(3, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  2 3  0

h(3, 6, 6, 6, 3) = −p^{4} + p^{5}

(3, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 4  3 4  0

(3, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  2 4  0

(3, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 4  3  2 4  3 4  p^{5}(p − 1)

(3, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 4  3 4  0

(3, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  2 4  0

(3, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 4  3 4  0

(3, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  2 4  p^{4}(p − 1)^{2}

h(3, 6, 6, 6, 4) = −p^{5} + p^{6}

(3, 6, 6, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  2 5  0

(3, 6, 6, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  2 5  p^{5}(p − 1)

h(3, 6, 6, 6, 5) = −p^{5} + p^{6}

\begin{matrix}(3, 6, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  3 3 & 0 \\ (3, 6, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  3 3 & 0 \\ (3, 6, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  3 3 & 0 \end{matrix}

\begin{matrix}(3, 6, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  3 4 & 0 \\ (3, 6, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  3 4 & 0 \\ (3, 6, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  3 4 & 0 \end{matrix}

\begin{matrix}(3, 6, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  1 5  3 5 & 0 \\ (3, 6, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  1 5  3 5 & 0 \\ (3, 6, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  3 5 & 0 \end{matrix}

(3, 6, 6, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  4 4  −p^{6}

h(3, 6, 6, 8, 4) = −p^{6}

(3, 6, 6, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  0 5  4 5  −p^{6}

h(3, 6, 6, 8, 5) = −p^{6}

(3, 6, 7, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  1 1  −p^{4}(p − 1)

(3, 6, 7, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  1 1  0

h(3, 6, 7, 4, 1) = p^{4} − p^{5}

(3, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 3  2 2  p^{4}(p − 1)^{2} ; (3, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  1 2  0 ; (3, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 3  2 2  −p^{5}(p − 1) ; (3, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  1 2  0 ; h(3, 6, 7, 4, 2) = p^{4} − p^{5} (3, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 3  2 3  p^{4}(p − 1)^{2} ; (3, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  1 3  −p^{4}(p − 1)^{2} ; (3, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 3  2 3  −p^{5}(p − 1) ; (3, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  1 3  0 ; h(3, 6, 7, 4, 3) = p^{5} − p^{6}

752

(3, 6, 7, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  1 4  −p^{5}(p − 1) ; (3, 6, 7, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  1 4  0 ; h(3, 6, 7, 4, 4) = p^{5} − p^{6} (3, 6, 7, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  1 1  −p^{4}(p − 1) ; (3, 6, 7, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  1 1  0 ; h(3, 6, 7, 5, 1) = p^{4} − p^{5}

753

\begin{matrix}(3, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 4  2 2 & 0 \\ (3, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  2 2 & 0 \\ (3, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  1 2 & 0 \\ (3, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 4  2 2 & 0 \\ (3, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  2 2 & 0 \\ (3, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  1 2 & 0 \end{matrix}

754

(3, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  2 3  0

(3, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  1 3  −p^{4}(p − 1)^{2}

(3, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 4  2 3  0

(3, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  2 3  0

(3, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  1 3  0

h(3, 6, 7, 5, 3) = −p^{4} + 2p^{5} − p^{6}

\begin{matrix}(3, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 4  2 4 & 0 \\ (3, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  2 4 & 0 \\ (3, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  1 4 & 0 \\ (3, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 4  2 4 & 0 \\ (3, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  2 4 & 0 \\ (3, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  1 4 & 0 \end{matrix} (3, 6, 7, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  1 5  p^{5}(p − 1) ; (3, 6, 7, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  1 5  0 ; h(3, 6, 7, 5, 5) = −p^{5} + p^{6}

756

(3, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  2 2  0

(3, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 5  2 2  p^{5}(p − 1)

(3, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  2 2  0

h(3, 6, 7, 6, 2) = −p^{4} + p^{5}

(3, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 5  2 3  0

(3, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  3 3  −p^{5}(p − 1)^{2}

(3, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  2 3  0

(3, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 4  3 3  −p^{5}(p − 1)^{2}

(3, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 5  2 3  0

(3, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  3 3  0

(3, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  2 3  0

h(3, 6, 7, 6, 3) = −p^{4} + p^{5} + p^{6} − p^{7}

(3, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 5  2 4  −p^{4}(p − 1)^{3}

(3, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 4  3 4  −p^{5}(p − 1)^{2}

(3, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  2 4  0

(3, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 4  3 4  −p^{5}(p − 1)^{2}

(3, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 5  2 4  p^{5}(p − 1)^{2}

(3, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 4  3 4  0

(3, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  2 4  0

h(3, 6, 7, 6, 4) = −p^{5} + 2p^{6} − p^{7}

(3, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 5  2 5  −p^{5}(p − 1)^{2} ; (3, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  2 5  0 ; (3, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 5  2 5  p^{6}(p − 1) ; (3, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  2 5  0 ; h(3, 6, 7, 6, 5) = −p^{5} + p^{6} (3, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 5  3 3  p^{5}(p − 1)^{2} ; (3, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  3 3  −p^{5}(p − 1)^{2} ; (3, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 5  3 3  −p^{6}(p − 1) ; (3, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  3 3  0 ; h(3, 6, 7, 7, 3) = p^{6} − p^{7}

760

\begin{matrix}(3, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 5  3 4 & 0 \\ (3, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  3 4 & 0 \\ (3, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 5  3 4 & 0 \\ (3, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  3 4 & 0 \end{matrix} (3, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  3  2 5  3 5  −p^{5}(p − 1)^{2} ; (3, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  3 5  p^{5}(p − 1)^{2} ; (3, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  3  2 5  3 5  p^{6}(p − 1) ; (3, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  3 5  0 ; h(3, 6, 7, 7, 5) = −p^{6} + p^{7}

761

(3, 6, 7, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  4 4  0

h(3, 6, 7, 8, 4) = −p^{6} + p^{7}

(3, 6, 7, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  1 5  4 5  p^{6}(p − 1)

(3, 6, 7, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  1 5  4 5  0

h(3, 6, 7, 8, 5) = −p^{6} + p^{7}

(3, 6, 8, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 4  2 2 −p^{5}(p − 1)

(3, 6, 8, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 4  2 2  p^{5}(p − 1)

cancel

\begin{matrix}(3, 6, 8, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 4  2 3 & 0 \\ (3, 6, 8, 5, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 4  2 3 & 0 \end{matrix}

(3, 6, 8, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 4  2 4 −p^{5}(p − 1)

cancel

(3, 6, 8, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  2 2 −p^{5}(p − 1)

(3, 6, 8, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  2 2  p^{5}(p − 1)

cancel

\begin{matrix}(3, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 4  3 3 & 0 \\ (3, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  2 3 & 0 \\ (3, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 4  3 3 & 0 \\ (3, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  2 3 & 0 \end{matrix}

(3, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  2 4 −p^{5}(p − 1)^{2}

(3, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 4  3 4  0

(3, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  2 4  p^{5}(p − 1)^{2}

cancel

(3, 6, 8, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  2 5 −p^{6}(p − 1)

(3, 6, 8, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  2 5  p^{6}(p − 1)

cancel

\begin{matrix}(3, 6, 8, 7, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  3 3 & 0 \\ (3, 6, 8, 7, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  3 3 & 0 \end{matrix}

\begin{matrix}(3, 6, 8, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  3 4 & 0 \\ (3, 6, 8, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  3 4 & 0 \end{matrix}
\begin{matrix}(3, 6, 8, 7, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  3 5 & 0 \\ (3, 6, 8, 7, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  3 5 & 0 \end{matrix}
(3, 6, 8, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  4 4  p^{6}(p − 1)
(3, 6, 8, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  4 4 −p^{6}(p − 1)

cancel

(3, 6, 8, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  2  1 5  4  2 5  4 5  p^{6}(p − 1)
(3, 6, 8, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  2 5  4 5 −p^{6}(p − 1)

cancel

h(3, 6, 9, 6, 3) = p^{7}

(3, 6, 9, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  3 4  3 4  p^{7}

h(3, 6, 9, 6, 4) = p^{7}

(3, 6, 9, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  3 5  3 3  p^{7}

h(3, 6, 9, 7, 3) = p^{7}

(3, 6, 9, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  3 5  3 4 0

(3, 6, 9, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  3 5  3 5  −p^{7}

h(3, 6, 9, 7, 5) = −p^{7}

(3, 6, 9, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  3 5  4 4  −p^{7}

h(3, 6, 9, 8, 4) = −p^{7}

(3, 6, 9, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  0 5  4  3 5  4 5  −p^{7}

h(3, 6, 9, 8, 5) = −p^{7}

h(3, 7, 5, 3, 1) = p^{5}

(3, 7, 5, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 3  1 2 0

(3, 7, 5, 3, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 3  1 3  −p^{5}

h(3, 7, 5, 3, 3) = −p^{5}

(3, 7, 5, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 4  1 1  p^{5}

h(3, 7, 5, 4, 1) = p^{5}

\begin{matrix}(3, 7, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 3  2 2 & 0 \\ (3, 7, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 4  1 2 & 0 \end{matrix}

(3, 7, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 3  2 3  0

(3, 7, 5, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 4  1 3  p^{5}(p − 1)

h(3, 7, 5, 4, 3) = −p^{5} + p^{6}

h(3, 7, 5, 4, 4) = p^{6}

(3, 7, 5, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 4  2 2 0

(3, 7, 5, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 4  2 3 0

(3, 7, 5, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 4  2 4 0

(3, 7, 5, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 4  3 3  −p^{6}

h(3, 7, 5, 6, 3) = −p^{6}

(3, 7, 5, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  1 4  3 4  −p^{6}

h(3, 7, 5, 6, 4) = −p^{6}

(3, 7, 6, 3, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 3  1 1  p^{5}

h(3, 7, 6, 3, 1) = p^{5}

(3, 7, 6, 3, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 3  1 2 0

h(3, 7, 6, 3, 3) = −p^{5}

(3, 7, 6, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  1 1 0

\begin{matrix}(3, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  2 3  2 2 & 0 \\ (3, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 3  2 2 & 0 \\ (3, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(3, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  2 3  2 3 & 0 \\ (3, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 3  2 3 & 0 \\ (3, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  1 3 & 0 \end{matrix}

(3, 7, 6, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  1 4 0

h(3, 7, 6, 5, 1) = −p^{5}

\begin{matrix}(3, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  2 4  2 2 & 0 \\ (3, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  2 2 & 0 \\ (3, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  1 2 & 0 \end{matrix}

(3, 7, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  2 4  2 3  0

(3, 7, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  2 3  0

(3, 7, 6, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  1 3  −p^{5}(p − 1)

h(3, 7, 6, 5, 3) = p^{5} − p^{6}

\begin{matrix}(3, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  2 4  2 4 & 0 \\ (3, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  2 4 & 0 \\ (3, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  1 4 & 0 \end{matrix}

(3, 7, 6, 5, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  1 5  p^{6}

h(3, 7, 6, 5, 5) = p^{6}

(3, 7, 6, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  2 2 0

\begin{matrix}(3, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  2 4  3 3 & 0 \\ (3, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  3 3 & 0 \\ (3, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  2 3 & 0 \end{matrix}

\begin{matrix}(3, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 4  3  2 4  3 4 & 0 \\ (3, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 4  3 4 & 0 \\ (3, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  2 4 & 0 \end{matrix}

(3, 7, 6, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  2 5 0

(3, 7, 6, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  3 3  p^{6}

h(3, 7, 6, 7, 3) = p^{6}

(3, 7, 6, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  3 4 0

(3, 7, 6, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  1 5  3 5  −p^{6}

h(3, 7, 6, 7, 5) = −p^{6}

(3, 7, 7, 4, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  1 1  −p^{5}

h(3, 7, 7, 4, 1) = −p^{5}

\begin{matrix}(3, 7, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 3  2 2 & 0 \\ (3, 7, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  1 2 & 0 \end{matrix}

(3, 7, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 3  2 3  0

(3, 7, 7, 4, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  1 3  −p^{5}(p − 1)

h(3, 7, 7, 4, 3) = p^{5} − p^{6}

(3, 7, 7, 4, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  1 4  −p^{6}

h(3, 7, 7, 4, 4) = −p^{6}

(3, 7, 7, 5, 1) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  1 1  −p^{5}

h(3, 7, 7, 5, 1) = −p^{5}

\begin{matrix}(3, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 4  2 2 & 0 \\ (3, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  2 2 & 0 \\ (3, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  1 2 & 0 \end{matrix}

(3, 7, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 4  2 3  0

(3, 7, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  2 3  0

(3, 7, 7, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  1 3  −p^{5}(p − 1)

h(3, 7, 7, 5, 3) = p^{5} − p^{6}

\begin{matrix}(3, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 4  2 4 & 0 \\ (3, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  2 4 & 0 \\ (3, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  1 4 & 0 \end{matrix}

h(3, 7, 7, 5, 5) = p^{6}

\begin{matrix}(3, 7, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 5  2 2 & 0 \\ (3, 7, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  2 2 & 0 \end{matrix}

(3, 7, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 4  3 3  0

(3, 7, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 5  2 3  0

(3, 7, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  3 3  −p^{6}(p − 1)

(3, 7, 7, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  2 3  0

h(3, 7, 7, 6, 3) = p^{6} − p^{7}

(3, 7, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 5  2 4  0

(3, 7, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 4  3 4  −p^{6}(p − 1)

(3, 7, 7, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  2 4  0

h(3, 7, 7, 6, 4) = p^{6} − p^{7}

\begin{matrix}(3, 7, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 5  2 5 & 0 \\ (3, 7, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  2 5 & 0 \end{matrix}

(3, 7, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 5  3 3  0

(3, 7, 7, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  3 3  −p^{6}(p − 1)

h(3, 7, 7, 7, 3) = p^{6} − p^{7}

\begin{matrix}(3, 7, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 5  3 4 & 0 \\ (3, 7, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  3 4 & 0 \end{matrix}

(3, 7, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  3  2 5  3 5  0

(3, 7, 7, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  3 5  p^{6}(p − 1)

h(3, 7, 7, 7, 5) = −p^{6} + p^{7}

(3, 7, 7, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  4 4  p^{7}

h(3, 7, 7, 8, 4) = p^{7}

(3, 7, 7, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  1 5  4 5  p^{7}

h(3, 7, 7, 8, 5) = p^{7}

(3, 7, 8, 5, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 4  2 2 0

(3, 7, 8, 5, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 4  2 3 0

(3, 7, 8, 5, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 4  2 4 0

(3, 7, 8, 6, 2) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  2 2 0

\begin{matrix}(3, 7, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 4  3 3 & 0 \\ (3, 7, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  2 3 & 0 \end{matrix}

\begin{matrix}(3, 7, 8, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 4  3 4 & 0 \\ (3, 7, 8, 6, 4) & 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  2 4 & 0 \end{matrix}

(3, 7, 8, 6, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  2 5 0

(3, 7, 8, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  3 3 0

(3, 7, 8, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  3 4 0

(3, 7, 8, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  3 5 0

(3, 7, 8, 8, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  4 4 0

(3, 7, 8, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  2 5  4 5 0

(3, 7, 9, 6, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  3 4  3 3  p^{7}

h(3, 7, 9, 6, 3) = p^{7}

(3, 7, 9, 6, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  3 4  3 4  p^{7}

h(3, 7, 9, 6, 4) = p^{7}

(3, 7, 9, 7, 3) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  3 5  3 3  p^{7}

h(3, 7, 9, 7, 3) = p^{7}

(3, 7, 9, 7, 4) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  3 5  3 4 0

(3, 7, 9, 7, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  3 5  3 5  −p^{7}

h(3, 7, 9, 7, 5) = −p^{7}

h(3, 7, 9, 8, 4) = −p^{7}

(3, 7, 9, 8, 5) 5  4  3  2  1  0 5  4  3  1  0 5  4  3  1 5  4  3 5  4 5  −p^{7}

h(3, 7, 9, 8, 5) = −p^{7}

(4, 3, 2, 1, 0) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 2  0 0  p^{2}

h(4, 3, 2, 1, 0) = p^{2}

(4, 3, 2, 1, 1) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 2  0 1 0

(4, 3, 2, 1, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 2  0 2  −p^{2}

h(4, 3, 2, 1, 2) = −p^{2}

(4, 3, 2, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 3  0 0  p^{2}

h(4, 3, 2, 2, 0) = p^{2}

\begin{matrix}(4, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 2  1 1 & 0 \\ (4, 3, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 3  0 1 & 0 \end{matrix}

(4, 3, 2, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 2  1 2  0

(4, 3, 2, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 3  0 2  p^{2}(p − 1)

h(4, 3, 2, 2, 2) = −p^{2} + p^{3}

(4, 3, 2, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 3  0 3  p^{3}

h(4, 3, 2, 2, 3) = p^{3}

(4, 3, 2, 3, 1) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 3  1 1 0

(4, 3, 2, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 3  1 2 0

(4, 3, 2, 3, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 3  1 3 0

h(4, 3, 2, 4, 2) = −p^{3}

(4, 3, 2, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  0 3  2 3  −p^{3}

h(4, 3, 2, 4, 3) = −p^{3}

(4, 3, 3, 1, 0) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 2  0 0  p^{2}

h(4, 3, 3, 1, 0) = p^{2}

(4, 3, 3, 1, 1) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 2  0 1 0

(4, 3, 3, 1, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 2  0 2  −p^{2}

h(4, 3, 3, 1, 2) = −p^{2}

(4, 3, 3, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  0 0 0

\begin{matrix}(4, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  1 2  1 1 & 0 \\ (4, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 2  1 1 & 0 \\ (4, 3, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(4, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  1 2  1 2 & 0 \\ (4, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 2  1 2 & 0 \\ (4, 3, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  0 2 & 0 \end{matrix}

(4, 3, 3, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  0 3 0

(4, 3, 3, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  0 0  −p^{2}

h(4, 3, 3, 3, 0) = −p^{2}

\begin{matrix}(4, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  1 3  1 1 & 0 \\ (4, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  1 1 & 0 \\ (4, 3, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  0 1 & 0 \end{matrix}

(4, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  1 3  1 2  0

(4, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  1 2  0

(4, 3, 3, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  0 2  −p^{2}(p − 1)

h(4, 3, 3, 3, 2) = p^{2} − p^{3}

\begin{matrix}(4, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  1 3  1 3 & 0 \\ (4, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  1 3 & 0 \\ (4, 3, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  0 3 & 0 \end{matrix}

h(4, 3, 3, 3, 4) = p^{3}

(4, 3, 3, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  1 1 0

\begin{matrix}(4, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  1 3  2 2 & 0 \\ (4, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  2 2 & 0 \\ (4, 3, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(4, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 3  2  1 3  2 3 & 0 \\ (4, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 3  2 3 & 0 \\ (4, 3, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  1 3 & 0 \end{matrix}

(4, 3, 3, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  1 4 0

h(4, 3, 3, 5, 2) = p^{3}

(4, 3, 3, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  2 3 0

(4, 3, 3, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  0 4  2 4  −p^{3}

h(4, 3, 3, 5, 4) = −p^{3}

(4, 3, 4, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 3  0 0  −p^{2}

h(4, 3, 4, 2, 0) = −p^{2}

\begin{matrix}(4, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 2  1 1 & 0 \\ (4, 3, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 3  0 1 & 0 \end{matrix}

(4, 3, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 2  1 2  0

(4, 3, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 3  0 2  −p^{2}(p − 1)

h(4, 3, 4, 2, 2) = p^{2} − p^{3}

h(4, 3, 4, 2, 3) = −p^{3}

(4, 3, 4, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  0 0  −p^{2}

h(4, 3, 4, 3, 0) = −p^{2}

\begin{matrix}(4, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 3  1 1 & 0 \\ (4, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 3  1 1 & 0 \\ (4, 3, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  0 1 & 0 \end{matrix}

(4, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 3  1 2  0

(4, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 3  1 2  0

(4, 3, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  0 2  −p^{2}(p − 1)

h(4, 3, 4, 3, 2) = p^{2} − p^{3}

\begin{matrix}(4, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 3  1 3 & 0 \\ (4, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 3  1 3 & 0 \\ (4, 3, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  0 3 & 0 \end{matrix}

(4, 3, 4, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  0 4  p^{3}

h(4, 3, 4, 3, 4) = p^{3}

\begin{matrix}(4, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 4  1 1 & 0 \\ (4, 3, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  1 1 & 0 \end{matrix}

(4, 3, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 3  2 2  0 ; (4, 3, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 4  1 2  0 ; (4, 3, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 3  2 2  −p^{3}(p − 1) ; (4, 3, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  1 2  0 ; h(4, 3, 4, 4, 2) = p^{3} − p^{4} (4, 3, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 3  2 3  0 ; (4, 3, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 4  1 3  0 ; (4, 3, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 3  2 3  −p^{3}(p − 1) ; (4, 3, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  1 3  0 ; h(4, 3, 4, 4, 3) = p^{3} − p^{4}

789

\begin{matrix}(4, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 4  1 4 & 0 \\ (4, 3, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  1 4 & 0 \end{matrix}

(4, 3, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 4  2 2  0

(4, 3, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  2 2  −p^{3}(p − 1)

h(4, 3, 4, 5, 2) = p^{3} − p^{4}

\begin{matrix}(4, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 4  2 3 & 0 \\ (4, 3, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  2 3 & 0 \end{matrix}

(4, 3, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  2  1 4  2 4  0

(4, 3, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  2 4  p^{3}(p − 1)

h(4, 3, 4, 5, 4) = −p^{3} + p^{4}

h(4, 3, 4, 6, 3) = p^{4}

(4, 3, 4, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  0 4  3 4  p^{4}

h(4, 3, 4, 6, 4) = p^{4}

(4, 3, 5, 3, 1) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 3  1 1 0

(4, 3, 5, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 3  1 2 0

(4, 3, 5, 3, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 3  1 3 0

(4, 3, 5, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  1 1 0

\begin{matrix}(4, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 3  2 2 & 0 \\ (4, 3, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(4, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 3  2 3 & 0 \\ (4, 3, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  1 3 & 0 \end{matrix}

(4, 3, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  1 4 0

(4, 3, 5, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  2 2 0

(4, 3, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  2 3 0

(4, 3, 5, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  2 4 0

(4, 3, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  3 3 0

(4, 3, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  1 4  3 4 0

h(4, 3, 6, 4, 2) = p^{4}

(4, 3, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  2 3  2 3  p^{4}

h(4, 3, 6, 4, 3) = p^{4}

(4, 3, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  2 4  2 2  p^{4}

h(4, 3, 6, 5, 2) = p^{4}

(4, 3, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  2 4  2 3 0

(4, 3, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  2 4  2 4  −p^{4}

h(4, 3, 6, 5, 4) = −p^{4}

(4, 3, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  2 4  3 3  −p^{4}

h(4, 3, 6, 6, 3) = −p^{4}

(4, 3, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  0 4  3  2 4  3 4  −p^{4}

h(4, 3, 6, 6, 4) = −p^{4}

h(4, 4, 2, 1, 0) = p^{2}

(4, 4, 2, 1, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 2  0 1 0

(4, 4, 2, 1, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 2  0 2  −p^{2}

h(4, 4, 2, 1, 2) = −p^{2}

(4, 4, 2, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 3  0 0  p^{2}

h(4, 4, 2, 2, 0) = p^{2}

\begin{matrix}(4, 4, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 2  1 1 & 0 \\ (4, 4, 2, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 3  0 1 & 0 \end{matrix}

(4, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 2  1 2  0

(4, 4, 2, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 3  0 2  p^{2}(p − 1)

h(4, 4, 2, 2, 2) = −p^{2} + p^{3}

h(4, 4, 2, 2, 3) = p^{3}

(4, 4, 2, 3, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 3  1 1 0

(4, 4, 2, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 3  1 2 0

(4, 4, 2, 3, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 3  1 3 0

(4, 4, 2, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 3  2 2  −p^{3}

h(4, 4, 2, 4, 2) = −p^{3}

(4, 4, 2, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  0 3  2 3  −p^{3}

h(4, 4, 2, 4, 3) = −p^{3}

(4, 4, 3, 1, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 2  0 0 0

(4, 4, 3, 1, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 2  0 1 0

(4, 4, 3, 1, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 2  0 2 0

(4, 4, 3, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  0 0 0

\begin{matrix}(4, 4, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 3  2  1 2  1 1 & 0 \\ (4, 4, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  1 2  1 1 & 0 \\ (4, 4, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 2  1 1 & 0 \\ (4, 4, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(4, 4, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 3  2  1 2  1 2 & 0 \\ (4, 4, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  1 2  1 2 & 0 \\ (4, 4, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 2  1 2 & 0 \\ (4, 4, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  0 2 & 0 \end{matrix}

(4, 4, 3, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  0 3 0

(4, 4, 3, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  0 0 0

\begin{matrix}(4, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 3  2  1 3  1 1 & 0 \\ (4, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  1 3  1 1 & 0 \\ (4, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  1 1 & 0 \\ (4, 4, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  0 1 & 0 \end{matrix} \begin{matrix}(4, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 3  2  1 3  1 2 & 0 \\ (4, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  1 3  1 2 & 0 \\ (4, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  1 2 & 0 \\ (4, 4, 3, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  0 2 & 0 \end{matrix}

798

\begin{matrix}(4, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 3  2  1 3  1 3 & 0 \\ (4, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  1 3  1 3 & 0 \\ (4, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  1 3 & 0 \\ (4, 4, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  0 3 & 0 \end{matrix}

(4, 4, 3, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  0 4 0

(4, 4, 3, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  1 1 0

\begin{matrix}(4, 4, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 3  2  1 3  2 2 & 0 \\ (4, 4, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  1 3  2 2 & 0 \\ (4, 4, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  2 2 & 0 \\ (4, 4, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(4, 4, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 3  2  1 3  2 3 & 0 \\ (4, 4, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 3  2  1 3  2 3 & 0 \\ (4, 4, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 3  2 3 & 0 \\ (4, 4, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  1 3 & 0 \end{matrix}

(4, 4, 3, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  1 4 0

(4, 4, 3, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  2 2 0

(4, 4, 3, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  2 3 0

(4, 4, 3, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  0 4  2 4 0

(4, 4, 4, 1, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 2  0 0  −p^{2}

h(4, 4, 4, 1, 0) = −p^{2}

(4, 4, 4, 1, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 2  0 1 0

(4, 4, 4, 1, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 2  0 2  p^{2}

h(4, 4, 4, 1, 2) = p^{2}

(4, 4, 4, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  0 0  p^{2}(p − 1)

(4, 4, 4, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  0 0  0

h(4, 4, 4, 2, 0) = −p^{2} + p^{3}

\begin{matrix}(4, 4, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 2  1 1 & 0 \\ (4, 4, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 2  1 1 & 0 \\ (4, 4, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  0 1 & 0 \\ (4, 4, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 2  1 1 & 0 \\ (4, 4, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  0 1 & 0 \end{matrix}

802

(4, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 2  1 2  0 ; (4, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 2  1 2  0 ; (4, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  0 2  p^{2}(p − 1)^{2} ; (4, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 2  1 2  0 ; (4, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  0 2  0 ; h(4, 4, 4, 2, 2) = p^{2} − 2p^{3} + p^{4} (4, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  0 3  p^{3}(p − 1) ; (4, 4, 4, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  0 3  0 ; h(4, 4, 4, 2, 3) = −p^{3} + p^{4}

803

(4, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  0 0  p^{2}(p − 1) ; (4, 4, 4, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  0 0 −p^{2}(p − 1) ; cancel \begin{matrix}(4, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 3  1 1 & 0 \\ (4, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 3  1 1 & 0 \\ (4, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  1 1 & 0 \\ (4, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  0 1 & 0 \\ (4, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  1 1 & 0 \\ (4, 4, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  0 1 & 0 \end{matrix}

804

(4, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 3  1 2  0
(4, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 3  1 2  0
(4, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  1 2  0
(4, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  0 2  p^{2}(p − 1)^{2}
(4, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  1 2  0
(4, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  0 2 −p^{2}(p − 1)^{2}

cancel

\begin{matrix}(4, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 3  1 3 & 0 \\ (4, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 3  1 3 & 0 \\ (4, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  1 3 & 0 \\ (4, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  0 3 & 0 \\ (4, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  1 3 & 0 \\ (4, 4, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  0 3 & 0 \end{matrix} (4, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  0 4 −p^{3}(p − 1) ; (4, 4, 4, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  0 4  p^{3}(p − 1) ; cancel

806

(4, 4, 4, 4, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  0 0  −p^{3} ; h(4, 4, 4, 4, 0) = −p^{3} \begin{matrix}(4, 4, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 4  1 1 & 0 \\ (4, 4, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 4  1 1 & 0 \\ (4, 4, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  1 1 & 0 \\ (4, 4, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  1 1 & 0 \\ (4, 4, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  0 1 & 0 \end{matrix}

807

(4, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 4  1 2  0

(4, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 3  2 2  0

(4, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 4  1 2  0

(4, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  2 2  p^{3}(p − 1)^{2}

(4, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  1 2  0

(4, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  2 2  0

(4, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  1 2  0

(4, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  0 2  −p^{3}(p − 1)

h(4, 4, 4, 4, 2) = 2p^{3} − 3p^{4} + p^{5}

(4, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 4  1 3  0

(4, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 3  2 3  0

(4, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 4  1 3  0

(4, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 3  2 3  p^{3}(p − 1)^{2}

(4, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  1 3  0

(4, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 3  2 3  0

(4, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  1 3  0

(4, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  0 3  0

h(4, 4, 4, 4, 3) = p^{3} − 2p^{4} + p^{5}

(4, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 4  1 4  0

(4, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  1 4  0

(4, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  1 4  0

(4, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  0 4  −p^{4}(p − 1)

h(4, 4, 4, 4, 4) = p^{4} − p^{5}

(4, 4, 4, 4, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  0 5  −p^{5}

h(4, 4, 4, 4, 5) = −p^{5}

(4, 4, 4, 5, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  1 1 0

(4, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 4  2 2  0

(4, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  2 2  p^{3}(p − 1)^{2}

(4, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  2 2  p^{3}(p − 1)

(4, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  1 2  0

h(4, 4, 4, 5, 2) = −p^{4} + p^{5}

\begin{matrix}(4, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  2  1 4  2 3 & 0 \\ (4, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 4  2 3 & 0 \\ (4, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  2 3 & 0 \\ (4, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  2 3 & 0 \\ (4, 4, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  1 3 & 0 \end{matrix}

812

(4, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  2  1 4  2 4  0

(4, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  2 4  −p^{3}(p − 1)^{2}

(4, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 4  2 4  −p^{3}(p − 1)

(4, 4, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  1 4  0

h(4, 4, 4, 5, 4) = p^{4} − p^{5}

(4, 4, 4, 5, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  1 5 0

(4, 4, 4, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  2 2  p^{4}

h(4, 4, 4, 6, 2) = p^{4}

(4, 4, 4, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  2 3  0

h(4, 4, 4, 6, 3) = p^{4} − p^{5}

(4, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  0 4  3 4 −p^{4}(p − 1)

(4, 4, 4, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  2 4  p^{4}(p − 1)

cancel

(4, 4, 4, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  0 5  2 5  p^{5}

h(4, 4, 4, 6, 5) = p^{5}

(4, 4, 5, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  0 0  p^{3}

h(4, 4, 5, 2, 0) = p^{3}

\begin{matrix}(4, 4, 5, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 2  1 1 & 0 \\ (4, 4, 5, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  0 1 & 0 \end{matrix}

(4, 4, 5, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  0 2  p^{3}(p − 1)

h(4, 4, 5, 2, 2) = −p^{3} + p^{4}

(4, 4, 5, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  0 3  p^{4}

h(4, 4, 5, 2, 3) = p^{4}

(4, 4, 5, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  0 0 0

\begin{matrix}(4, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 3  1 1 & 0 \\ (4, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 3  1 1 & 0 \\ (4, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 3  1 1 & 0 \\ (4, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  1 1 & 0 \\ (4, 4, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  0 1 & 0 \end{matrix}

816

\begin{matrix}(4, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 3  1 2 & 0 \\ (4, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 3  1 2 & 0 \\ (4, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 3  1 2 & 0 \\ (4, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  1 2 & 0 \\ (4, 4, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  0 2 & 0 \end{matrix}

817

\begin{matrix}(4, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 3  1 3 & 0 \\ (4, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 3  1 3 & 0 \\ (4, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 3  1 3 & 0 \\ (4, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  1 3 & 0 \\ (4, 4, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  0 3 & 0 \end{matrix}

(4, 4, 5, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  0 4 0

(4, 4, 5, 4, 0) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  0 0  −p^{3}

h(4, 4, 5, 4, 0) = −p^{3}

\begin{matrix}(4, 4, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 4  1 1 & 0 \\ (4, 4, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  1 1 & 0 \\ (4, 4, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 4  1 1 & 0 \\ (4, 4, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  1 1 & 0 \\ (4, 4, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  0 1 & 0 \end{matrix}

819

(4, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 4  1 2  0

(4, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 3  2 2  0

(4, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  1 2  0

(4, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 3  2 2  0

(4, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 4  1 2  0

(4, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  2 2  p^{4}(p − 1)

(4, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  1 2  0

(4, 4, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  0 2  −p^{3}(p − 1)

h(4, 4, 5, 4, 2) = p^{3} − 2p^{4} + p^{5}

(4, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 4  1 3  0

(4, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 3  2 3  0

(4, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  1 3  0

(4, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 3  2 3  0

(4, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 4  1 3  0

(4, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 3  2 3  p^{4}(p − 1)

(4, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  1 3  0

(4, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  0 3  0

h(4, 4, 5, 4, 3) = −p^{4} + p^{5}

(4, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  1 4  0

(4, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 4  1 4  0

(4, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  1 4  0

(4, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  0 4  −p^{4}(p − 1)

h(4, 4, 5, 4, 4) = p^{4} − p^{5}

(4, 4, 5, 4, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  0 5  −p^{5}

h(4, 4, 5, 4, 5) = −p^{5}

\begin{matrix}(4, 4, 5, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  1 1 & 0 \\ (4, 4, 5, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  1 1 & 0 \end{matrix}

\begin{matrix}(4, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 4  2 2 & 0 \\ (4, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  2 2 & 0 \\ (4, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 4  2 2 & 0 \\ (4, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  1 2 & 0 \\ (4, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  2 2 & 0 \\ (4, 4, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  1 2 & 0 \end{matrix}

823

\begin{matrix}(4, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 4  2 3 & 0 \\ (4, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  2 3 & 0 \\ (4, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 4  2 3 & 0 \\ (4, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  1 3 & 0 \\ (4, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  2 3 & 0 \\ (4, 4, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  1 3 & 0 \end{matrix}

824

\begin{matrix}(4, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 4  2 4 & 0 \\ (4, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  2 4 & 0 \\ (4, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 4  2 4 & 0 \\ (4, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  1 4 & 0 \\ (4, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  2 4 & 0 \\ (4, 4, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  1 4 & 0 \end{matrix} \begin{matrix}(4, 4, 5, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  1 5 & 0 \\ (4, 4, 5, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  1 5 & 0 \end{matrix}

825

(4, 4, 5, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  2 2  0 ; (4, 4, 5, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  2 2  −p^{4}(p − 1) ; h(4, 4, 5, 6, 2) = p^{4} − p^{5} (4, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  1 4  3 3  0 ; (4, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  3 3  0 ; (4, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  2 3  0 ; (4, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  3 3  p^{5}(p − 1) ; (4, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  2 3  0 ; h(4, 4, 5, 6, 3) = −p^{5} + p^{6}

826

(4, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  1 4  3 4  0

(4, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  2 4  0

(4, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 4  3 4  p^{5}(p − 1)

(4, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  2 4  −p^{4}(p − 1)^{2}

h(4, 4, 5, 6, 4) = −p^{4} + p^{5}

(4, 4, 5, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  2  1 5  2 5  0

(4, 4, 5, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  2 5  −p^{5}(p − 1)

h(4, 4, 5, 6, 5) = p^{5} − p^{6}

(4, 4, 5, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  3 3  p^{6}

h(4, 4, 5, 7, 3) = p^{6}

(4, 4, 5, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  3 4 0

(4, 4, 5, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  0 5  3 5  −p^{6}

h(4, 4, 5, 7, 5) = −p^{6}

(4, 4, 6, 3, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 3  1 1 0

(4, 4, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 3  1 2 0

(4, 4, 6, 3, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 3  1 3 0

(4, 4, 6, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  1 1 0

(4, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  2 3  2 2  0 ; (4, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  2 3  2 2  −p^{4}(p − 1) ; (4, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 3  2 2  0 ; (4, 4, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  1 2  0 ; h(4, 4, 6, 4, 2) = p^{4} − p^{5} (4, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  2 3  2 3  0 ; (4, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  2 3  2 3  −p^{4}(p − 1) ; (4, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 3  2 3  0 ; (4, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  1 3  0 ; h(4, 4, 6, 4, 3) = p^{4} − p^{5}

829

(4, 4, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  1 4 0

(4, 4, 6, 5, 1) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  1 1 0

(4, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  2 4  2 2  0

(4, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  2 4  2 2  −p^{4}(p − 1)

(4, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  2 2  0

(4, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  1 2  0

h(4, 4, 6, 5, 2) = p^{4} − p^{5}

\begin{matrix}(4, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  2 4  2 3 & 0 \\ (4, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  2 4  2 3 & 0 \\ (4, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  2 3 & 0 \\ (4, 4, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  1 3 & 0 \end{matrix}

(4, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  2 4  2 4  0

(4, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  2 4  2 4  p^{4}(p − 1)

(4, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  2 4  0

(4, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  1 4  0

h(4, 4, 6, 5, 4) = −p^{4} + p^{5}

(4, 4, 6, 5, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  1 5 0

(4, 4, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  2 2 0 (4, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 4  3  2  1 4  3  2 4  3 3  0 ; (4, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  2 4  3 3  p^{4}(p − 1) ; (4, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  3 3  0 ; (4, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  2 3  0 ; h(4, 4, 6, 6, 3) = −p^{4} + p^{5}

832

(4, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 4  3  2 4  3 4  p^{4}(p − 1)

(4, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 4  3 4  0

(4, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  2 4  0

h(4, 4, 6, 6, 4) = −p^{4} + p^{5}

(4, 4, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  2 5 0

(4, 4, 6, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  3 3 0

(4, 4, 6, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  3 4 0

(4, 4, 6, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  1 5  3 5 0

h(4, 4, 7, 4, 2) = −p^{5}

(4, 4, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 3  2 3  −p^{5}

h(4, 4, 7, 4, 3) = −p^{5}

(4, 4, 7, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 4  2 2 0

(4, 4, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 4  2 3 0

(4, 4, 7, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 4  2 4 0

(4, 4, 7, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 5  2 2  p^{5}

h(4, 4, 7, 6, 2) = p^{5}

(4, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 4  3 3  −p^{5}(p − 1)

(4, 4, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 5  2 3  0

h(4, 4, 7, 6, 3) = p^{5} − p^{6}

(4, 4, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 5  2 4  p^{5}(p − 1)

cancel

(4, 4, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 5  2 5  p^{6}

h(4, 4, 7, 6, 5) = p^{6}

(4, 4, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 5  3 3  −p^{6}

h(4, 4, 7, 7, 3) = −p^{6}

(4, 4, 7, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 5  3 4 0

(4, 4, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  0 5  3  2 5  3 5  p^{6}

h(4, 4, 7, 7, 5) = p^{6}

(4, 5, 3, 1, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 2  0 0  −p^{2}

h(4, 5, 3, 1, 0) = −p^{2}

(4, 5, 3, 1, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 2  0 1 0

h(4, 5, 3, 1, 2) = p^{2}

(4, 5, 3, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  0 0 0

\begin{matrix}(4, 5, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 3  2  1 2  1 1 & 0 \\ (4, 5, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 2  1 1 & 0 \\ (4, 5, 3, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(4, 5, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 3  2  1 2  1 2 & 0 \\ (4, 5, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 2  1 2 & 0 \\ (4, 5, 3, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  0 2 & 0 \end{matrix}

(4, 5, 3, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  0 3 0

h(4, 5, 3, 3, 0) = p^{2}

\begin{matrix}(4, 5, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 3  2  1 3  1 1 & 0 \\ (4, 5, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  1 1 & 0 \\ (4, 5, 3, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  0 1 & 0 \end{matrix}

(4, 5, 3, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 3  2  1 3  1 2  0

(4, 5, 3, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  1 2  0

(4, 5, 3, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  0 2  p^{2}(p − 1)

h(4, 5, 3, 3, 2) = −p^{2} + p^{3}

\begin{matrix}(4, 5, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 3  2  1 3  1 3 & 0 \\ (4, 5, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  1 3 & 0 \\ (4, 5, 3, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  0 3 & 0 \end{matrix}

(4, 5, 3, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  0 4  −p^{3}

h(4, 5, 3, 3, 4) = −p^{3}

(4, 5, 3, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  1 1 0

\begin{matrix}(4, 5, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 3  2  1 3  2 2 & 0 \\ (4, 5, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  2 2 & 0 \\ (4, 5, 3, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  1 2 & 0 \end{matrix}

\begin{matrix}(4, 5, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 3  2  1 3  2 3 & 0 \\ (4, 5, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 3  2 3 & 0 \\ (4, 5, 3, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  1 3 & 0 \end{matrix}

(4, 5, 3, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  1 4 0

(4, 5, 3, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  2 2  −p^{3}

h(4, 5, 3, 5, 2) = −p^{3}

(4, 5, 3, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  2 3 0

(4, 5, 3, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  0 4  2 4  p^{3}

h(4, 5, 3, 5, 4) = p^{3}

(4, 5, 4, 1, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 2  0 0  −p^{2}

h(4, 5, 4, 1, 0) = −p^{2}

(4, 5, 4, 1, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 2  0 1 0

(4, 5, 4, 1, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 2  0 2  p^{2}

h(4, 5, 4, 1, 2) = p^{2}

\begin{matrix}(4, 5, 4, 2, 0) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  0 0 & 0 \\ (4, 5, 4, 2, 0) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  0 0 & 0 \end{matrix}

\begin{matrix}(4, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 2  1 1 & 0 \\ (4, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 2  1 1 & 0 \\ (4, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  0 1 & 0 \\ (4, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 2  1 1 & 0 \\ (4, 5, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(4, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 2  1 2 & 0 \\ (4, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 2  1 2 & 0 \\ (4, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  0 2 & 0 \\ (4, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 2  1 2 & 0 \\ (4, 5, 4, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  0 2 & 0 \end{matrix}

\begin{matrix}(4, 5, 4, 2, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  0 3 & 0 \\ (4, 5, 4, 2, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  0 3 & 0 \end{matrix}

(4, 5, 4, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  0 0  0

(4, 5, 4, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  0 0  −p^{2}(p − 1)

h(4, 5, 4, 3, 0) = p^{2} − p^{3}

\begin{matrix}(4, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 3  1 1 & 0 \\ (4, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 3  1 1 & 0 \\ (4, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  1 1 & 0 \\ (4, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  0 1 & 0 \\ (4, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  1 1 & 0 \\ (4, 5, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  0 1 & 0 \end{matrix}

842

(4, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 3  1 2  0

(4, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  1 2  0

(4, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  0 2  0

(4, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  1 2  0

(4, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  0 2  −p^{2}(p − 1)^{2}

h(4, 5, 4, 3, 2) = −p^{2} + 2p^{3} − p^{4}

\begin{matrix}(4, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 3  1 3 & 0 \\ (4, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 3  1 3 & 0 \\ (4, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  1 3 & 0 \\ (4, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  0 3 & 0 \\ (4, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  1 3 & 0 \\ (4, 5, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  0 3 & 0 \end{matrix} (4, 5, 4, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  0 4  0 ; (4, 5, 4, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  0 4  p^{3}(p − 1) ; h(4, 5, 4, 3, 4) = −p^{3} + p^{4}

844

(4, 5, 4, 4, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  0 0  −p^{3} ; h(4, 5, 4, 4, 0) = −p^{3} \begin{matrix}(4, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 4  1 1 & 0 \\ (4, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 4  1 1 & 0 \\ (4, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  1 1 & 0 \\ (4, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  1 1 & 0 \\ (4, 5, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  0 1 & 0 \end{matrix}

845

(4, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 4  1 2  0

(4, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 3  2 2  0

(4, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 4  1 2  0

(4, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  2 2  0

(4, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  1 2  0

(4, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  2 2  0

(4, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  1 2  0

(4, 5, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  0 2  −p^{3}(p − 1)

h(4, 5, 4, 4, 2) = p^{3} − p^{4}

\begin{matrix}(4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 3  2 3 & 0 \\ (4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 4  1 3 & 0 \\ (4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 3  2 3 & 0 \\ (4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 4  1 3 & 0 \\ (4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 3  2 3 & 0 \\ (4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  1 3 & 0 \\ (4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 3  2 3 & 0 \\ (4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  1 3 & 0 \\ (4, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  0 3 & 0 \end{matrix}

847

(4, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 4  1 4  0

(4, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  1 4  0

(4, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  1 4  0

(4, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  0 4  −p^{4}(p − 1)

h(4, 5, 4, 4, 4) = p^{4} − p^{5}

(4, 5, 4, 4, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  0 5  −p^{5}

h(4, 5, 4, 4, 5) = −p^{5}

(4, 5, 4, 5, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  1 1 0

(4, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 4  2 2  0

(4, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  2 2  0

(4, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  2 2  p^{3}(p − 1)

(4, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  1 2  0

h(4, 5, 4, 5, 2) = −p^{3} + p^{4}

\begin{matrix}(4, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  2  1 4  2 3 & 0 \\ (4, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 4  2 3 & 0 \\ (4, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  2 3 & 0 \\ (4, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  2 3 & 0 \\ (4, 5, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  1 3 & 0 \end{matrix}

850

(4, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  2  1 4  2 4  0

(4, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  2 4  0

(4, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 4  2 4  −p^{3}(p − 1)

(4, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  1 4  0

h(4, 5, 4, 5, 4) = p^{3} − p^{4}

(4, 5, 4, 5, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  1 5 0

(4, 5, 4, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  2 2  p^{4}

h(4, 5, 4, 6, 2) = p^{4}

\begin{matrix}(4, 5, 4, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  3 3 & 0 \\ (4, 5, 4, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  2 3 & 0 \end{matrix}

(4, 5, 4, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  0 4  3 4  0

(4, 5, 4, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  2 4  p^{4}(p − 1)

h(4, 5, 4, 6, 4) = −p^{4} + p^{5}

(4, 5, 4, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  0 5  2 5  p^{5}

h(4, 5, 4, 6, 5) = p^{5}

(4, 5, 5, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  0 0 0

\begin{matrix}(4, 5, 5, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 2  1 1 & 0 \\ (4, 5, 5, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 2  1 1 & 0 \\ (4, 5, 5, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  0 1 & 0 \end{matrix}

\begin{matrix}(4, 5, 5, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 2  1 2 & 0 \\ (4, 5, 5, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 2  1 2 & 0 \\ (4, 5, 5, 2, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  0 2 & 0 \end{matrix}

(4, 5, 5, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  0 3 0

(4, 5, 5, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  0 0 0

\begin{matrix}(4, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 3  1 1 & 0 \\ (4, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 3  1 1 & 0 \\ (4, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 3  1 1 & 0 \\ (4, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 3  1 1 & 0 \\ (4, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  1 1 & 0 \\ (4, 5, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  0 1 & 0 \end{matrix}

854

\begin{matrix}(4, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 3  1 2 & 0 \\ (4, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 3  1 2 & 0 \\ (4, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 3  1 2 & 0 \\ (4, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 3  1 2 & 0 \\ (4, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  1 2 & 0 \\ (4, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  0 2 & 0 \end{matrix}

855

\begin{matrix}(4, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 3  1 3 & 0 \\ (4, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 3  1 3 & 0 \\ (4, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 3  1 3 & 0 \\ (4, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 3  1 3 & 0 \\ (4, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  1 3 & 0 \\ (4, 5, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  0 3 & 0 \end{matrix}

(4, 5, 5, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  0 4 0

(4, 5, 5, 4, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  0 0 0

\begin{matrix}(4, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  1 1 & 0 \\ (4, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 4  1 1 & 0 \\ (4, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  1 1 & 0 \\ (4, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 4  1 1 & 0 \\ (4, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  1 1 & 0 \\ (4, 5, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  0 1 & 0 \end{matrix}

857

\begin{matrix}(4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 3  2 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  1 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 3  2 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 4  1 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 3  2 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  1 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 3  2 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 4  1 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  2 2 & 0 \end{matrix}

858

\begin{matrix}(4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  1 2 & 0 \\ (4, 5, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  0 2 & 0 \end{matrix}

859

\begin{matrix}(4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 3  2 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  1 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 3  2 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 4  1 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 3  2 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  1 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 3  2 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 4  1 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 3  2 3 & 0 \end{matrix}

860

\begin{matrix}(4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  1 3 & 0 \\ (4, 5, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  0 3 & 0 \end{matrix}

\begin{matrix}(4, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  1 4 & 0 \\ (4, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 4  1 4 & 0 \\ (4, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  1 4 & 0 \\ (4, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 4  1 4 & 0 \\ (4, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  1 4 & 0 \\ (4, 5, 5, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  0 4 & 0 \end{matrix}

(4, 5, 5, 4, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  0 5 0

\begin{matrix}(4, 5, 5, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  1 1 & 0 \\ (4, 5, 5, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  1 1 & 0 \\ (4, 5, 5, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  1 1 & 0 \end{matrix}

862

\begin{matrix}(4, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  2 2 & 0 \\ (4, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 4  2 2 & 0 \\ (4, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  1 2 & 0 \\ (4, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  2 2 & 0 \\ (4, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 4  2 2 & 0 \\ (4, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  1 2 & 0 \\ (4, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  2 2 & 0 \\ (4, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  1 2 & 0 \end{matrix}

863

\begin{matrix}(4, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  2 3 & 0 \\ (4, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 4  2 3 & 0 \\ (4, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  1 3 & 0 \\ (4, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  2 3 & 0 \\ (4, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 4  2 3 & 0 \\ (4, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  1 3 & 0 \\ (4, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  2 3 & 0 \\ (4, 5, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  1 3 & 0 \end{matrix}

864

\begin{matrix}(4, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  2 4 & 0 \\ (4, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 4  2 4 & 0 \\ (4, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  1 4 & 0 \\ (4, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  2 4 & 0 \\ (4, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 4  2 4 & 0 \\ (4, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  1 4 & 0 \\ (4, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  2 4 & 0 \\ (4, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  1 4 & 0 \end{matrix}

865

\begin{matrix}(4, 5, 5, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  1 5 & 0 \\ (4, 5, 5, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  1 5 & 0 \\ (4, 5, 5, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  1 5 & 0 \end{matrix} \begin{matrix}(4, 5, 5, 6, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  2 2 & 0 \\ (4, 5, 5, 6, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  2 2 & 0 \\ (4, 5, 5, 6, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  2 2 & 0 \end{matrix}

866

\begin{matrix}(4, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  3 3 & 0 \\ (4, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  2 3 & 0 \\ (4, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  3 3 & 0 \\ (4, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  2 3 & 0 \\ (4, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  3 3 & 0 \\ (4, 5, 5, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  2 3 & 0 \end{matrix}

867

\begin{matrix}(4, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  1 4  3 4 & 0 \\ (4, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  2 4 & 0 \\ (4, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  1 4  3 4 & 0 \\ (4, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  2 4 & 0 \\ (4, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 4  3 4 & 0 \\ (4, 5, 5, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  2 4 & 0 \end{matrix} \begin{matrix}(4, 5, 5, 6, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  2  1 5  2 5 & 0 \\ (4, 5, 5, 6, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  2  1 5  2 5 & 0 \\ (4, 5, 5, 6, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  2 5 & 0 \end{matrix}

868

(4, 5, 5, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  3 3 0

(4, 5, 5, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  3 4 0

(4, 5, 5, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  0 5  3 5 0

(4, 5, 6, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  0 0  p^{3}

h(4, 5, 6, 3, 0) = p^{3}

\begin{matrix}(4, 5, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 3  1 1 & 0 \\ (4, 5, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 3  1 1 & 0 \\ (4, 5, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  0 1 & 0 \end{matrix}

(4, 5, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 3  1 2  0

(4, 5, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  0 2  p^{3}(p − 1)

h(4, 5, 6, 3, 2) = −p^{3} + p^{4}

\begin{matrix}(4, 5, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 3  1 3 & 0 \\ (4, 5, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 3  1 3 & 0 \\ (4, 5, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  0 3 & 0 \end{matrix}

(4, 5, 6, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  0 4  −p^{4}

h(4, 5, 6, 3, 4) = −p^{4}

(4, 5, 6, 4, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  0 0  p^{3}

h(4, 5, 6, 4, 0) = p^{3}

\begin{matrix}(4, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 4  1 1 & 0 \\ (4, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  1 1 & 0 \\ (4, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  1 1 & 0 \\ (4, 5, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  0 1 & 0 \end{matrix}

871

(4, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 3  2 2  0

(4, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 4  1 2  0

(4, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  2 3  2 2  0

(4, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 3  2 2  0

(4, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  1 2  0

(4, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  1 2  0

(4, 5, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  0 2  p^{3}(p − 1)

h(4, 5, 6, 4, 2) = −p^{3} + p^{4}

\begin{matrix}(4, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  2 3  2 3 & 0 \\ (4, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 3  2 3 & 0 \\ (4, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 4  1 3 & 0 \\ (4, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  2 3  2 3 & 0 \\ (4, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 3  2 3 & 0 \\ (4, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  1 3 & 0 \\ (4, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  1 3 & 0 \\ (4, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  0 3 & 0 \end{matrix}

873

(4, 5, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  1 4  0

(4, 5, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  1 4  0

(4, 5, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  0 4  p^{4}(p − 1)

h(4, 5, 6, 4, 4) = −p^{4} + p^{5}

(4, 5, 6, 4, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  0 5  p^{5}

h(4, 5, 6, 4, 5) = p^{5}

\begin{matrix}(4, 5, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  1 1 & 0 \\ (4, 5, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  1 1 & 0 \\ (4, 5, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  1 1 & 0 \end{matrix}

(4, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 4  2 2  0

(4, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  1 2  0

(4, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  2 4  2 2  0

(4, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  2 2  0

(4, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  1 2  0

(4, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  2 2  p^{4}(p − 1)

(4, 5, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  1 2  0

h(4, 5, 6, 5, 2) = −p^{4} + p^{5}

\begin{matrix}(4, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  2 4  2 3 & 0 \\ (4, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 4  2 3 & 0 \\ (4, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  1 3 & 0 \\ (4, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  2 4  2 3 & 0 \\ (4, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  2 3 & 0 \\ (4, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  1 3 & 0 \\ (4, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  2 3 & 0 \\ (4, 5, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  1 3 & 0 \end{matrix}

876

(4, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 4  2 4  0

(4, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  1 4  0

(4, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  2 4  2 4  0

(4, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  2 4  0

(4, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  1 4  0

(4, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  2 4  −p^{4}(p − 1)

(4, 5, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  1 4  0

h(4, 5, 6, 5, 4) = p^{4} − p^{5}

\begin{matrix}(4, 5, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  1 5 & 0 \\ (4, 5, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  1 5 & 0 \\ (4, 5, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  1 5 & 0 \end{matrix} (4, 5, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  2 2  0 ; (4, 5, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  2 2  0 ; (4, 5, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  2 2  p^{4}(p − 1) ; h(4, 5, 6, 6, 2) = −p^{4} + p^{5}

878

\begin{matrix}(4, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 4  3  2 4  3 3 & 0 \\ (4, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 4  3 3 & 0 \\ (4, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  2 3 & 0 \\ (4, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  2 4  3 3 & 0 \\ (4, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  3 3 & 0 \\ (4, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  2 3 & 0 \\ (4, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  3 3 & 0 \\ (4, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  2 3 & 0 \end{matrix}

879

(4, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 4  3 4  0

(4, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  2 4  0

(4, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 4  3  2 4  3 4  0

(4, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 4  3 4  0

(4, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  2 4  0

(4, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 4  3 4  0

(4, 5, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  2 4  p^{4}(p − 1)^{2}

h(4, 5, 6, 6, 4) = p^{4} − 2p^{5} + p^{6}

(4, 5, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  2 5  0

(4, 5, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  2 5  p^{5}(p − 1)

h(4, 5, 6, 6, 5) = −p^{5} + p^{6}

\begin{matrix}(4, 5, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  3 3 & 0 \\ (4, 5, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  3 3 & 0 \\ (4, 5, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  3 3 & 0 \end{matrix}

\begin{matrix}(4, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  3 4 & 0 \\ (4, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  3 4 & 0 \\ (4, 5, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  3 4 & 0 \end{matrix}

\begin{matrix}(4, 5, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  1 5  3 5 & 0 \\ (4, 5, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  1 5  3 5 & 0 \\ (4, 5, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  3 5 & 0 \end{matrix}

(4, 5, 6, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  4 4  −p^{6}

h(4, 5, 6, 8, 4) = −p^{6}

(4, 5, 6, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  0 5  4 5  −p^{6}

h(4, 5, 6, 8, 5) = −p^{6}

(4, 5, 7, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  1 1 0

\begin{matrix}(4, 5, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 3  2 2 & 0 \\ (4, 5, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 3  2 2 & 0 \\ (4, 5, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(4, 5, 7, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 3  2 3 & 0 \\ (4, 5, 7, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 3  2 3 & 0 \\ (4, 5, 7, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  1 3 & 0 \end{matrix}

(4, 5, 7, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  1 4 0

(4, 5, 7, 5, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  1 1 0

\begin{matrix}(4, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 4  2 2 & 0 \\ (4, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 4  2 2 & 0 \\ (4, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  2 2 & 0 \\ (4, 5, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  1 2 & 0 \end{matrix} \begin{matrix}(4, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 4  2 3 & 0 \\ (4, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 4  2 3 & 0 \\ (4, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  2 3 & 0 \\ (4, 5, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  1 3 & 0 \end{matrix}

884

\begin{matrix}(4, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 4  2 4 & 0 \\ (4, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 4  2 4 & 0 \\ (4, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  2 4 & 0 \\ (4, 5, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  1 4 & 0 \end{matrix}

(4, 5, 7, 5, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  1 5 0

\begin{matrix}(4, 5, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 5  2 2 & 0 \\ (4, 5, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 5  2 2 & 0 \\ (4, 5, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  2 2 & 0 \end{matrix}

\begin{matrix}(4, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 4  3 3 & 0 \\ (4, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 5  2 3 & 0 \\ (4, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 4  3 3 & 0 \\ (4, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 5  2 3 & 0 \\ (4, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  3 3 & 0 \\ (4, 5, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  2 3 & 0 \end{matrix}

886

\begin{matrix}(4, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 4  3 4 & 0 \\ (4, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 5  2 4 & 0 \\ (4, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 4  3 4 & 0 \\ (4, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 5  2 4 & 0 \\ (4, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 4  3 4 & 0 \\ (4, 5, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  2 4 & 0 \end{matrix} \begin{matrix}(4, 5, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 5  2 5 & 0 \\ (4, 5, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 5  2 5 & 0 \\ (4, 5, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  2 5 & 0 \end{matrix}

887

\begin{matrix}(4, 5, 7, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 5  3 3 & 0 \\ (4, 5, 7, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 5  3 3 & 0 \\ (4, 5, 7, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  3 3 & 0 \end{matrix}

\begin{matrix}(4, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 5  3 4 & 0 \\ (4, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 5  3 4 & 0 \\ (4, 5, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  3 4 & 0 \end{matrix}

\begin{matrix}(4, 5, 7, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  3  2  1 5  3  2 5  3 5 & 0 \\ (4, 5, 7, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  3  2 5  3 5 & 0 \\ (4, 5, 7, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  3 5 & 0 \end{matrix}

(4, 5, 7, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  4 4 0

(4, 5, 7, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  1 5  4 5 0

(4, 5, 8, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 4  2 2  −p^{5}

h(4, 5, 8, 5, 2) = −p^{5}

(4, 5, 8, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 4  2 3 0

(4, 5, 8, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 4  2 4  p^{5}

h(4, 5, 8, 5, 4) = p^{5}

(4, 5, 8, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  2 2  −p^{5}

h(4, 5, 8, 6, 2) = −p^{5}

\begin{matrix}(4, 5, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 4  3 3 & 0 \\ (4, 5, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  2 3 & 0 \end{matrix}

(4, 5, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  2 4  −p^{5}(p − 1)

h(4, 5, 8, 6, 4) = p^{5} − p^{6}

(4, 5, 8, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  2 5  −p^{6}

h(4, 5, 8, 6, 5) = −p^{6}

(4, 5, 8, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  3 3 0

(4, 5, 8, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  3 4 0

(4, 5, 8, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  3 5 0

(4, 5, 8, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  4 4  p^{6}

h(4, 5, 8, 8, 4) = p^{6}

(4, 5, 8, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  0 5  4  2 5  4 5  p^{6}

h(4, 5, 8, 8, 5) = p^{6}

h(4, 6, 4, 2, 0) = −p^{3}

\begin{matrix}(4, 6, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 2  1 1 & 0 \\ (4, 6, 4, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 3  0 1 & 0 \end{matrix}

(4, 6, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 2  1 2  0

(4, 6, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 3  0 2  −p^{3}(p − 1)

h(4, 6, 4, 2, 2) = p^{3} − p^{4}

(4, 6, 4, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 3  0 3  −p^{4}

h(4, 6, 4, 2, 3) = −p^{4}

(4, 6, 4, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  0 0  −p^{3}

h(4, 6, 4, 3, 0) = −p^{3}

\begin{matrix}(4, 6, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 3  1 1 & 0 \\ (4, 6, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 3  1 1 & 0 \\ (4, 6, 4, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  0 1 & 0 \end{matrix}

(4, 6, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 3  1 2  0

(4, 6, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 3  1 2  0

(4, 6, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  0 2  −p^{3}(p − 1)

h(4, 6, 4, 3, 2) = p^{3} − p^{4}

\begin{matrix}(4, 6, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 3  1 3 & 0 \\ (4, 6, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 3  1 3 & 0 \\ (4, 6, 4, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  0 3 & 0 \end{matrix}

h(4, 6, 4, 3, 4) = p^{4}

\begin{matrix}(4, 6, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 4  1 1 & 0 \\ (4, 6, 4, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  1 1 & 0 \end{matrix}

(4, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 3  2 2  0

(4, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 4  1 2  0

(4, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 3  2 2  −p^{4}(p − 1)

(4, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  1 2  0

h(4, 6, 4, 4, 2) = p^{4} − p^{5}

(4, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 4  1 3  0

(4, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 3  2 3  −p^{4}(p − 1)

(4, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  1 3  0

h(4, 6, 4, 4, 3) = p^{4} − p^{5}

\begin{matrix}(4, 6, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 4  1 4 & 0 \\ (4, 6, 4, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  1 4 & 0 \end{matrix}

(4, 6, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 4  2 2  0

(4, 6, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  2 2  −p^{4}(p − 1)

h(4, 6, 4, 5, 2) = p^{4} − p^{5}

\begin{matrix}(4, 6, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 4  2 3 & 0 \\ (4, 6, 4, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  2 3 & 0 \end{matrix}

(4, 6, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  2  1 4  2 4  0

(4, 6, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  2 4  p^{4}(p − 1)

h(4, 6, 4, 5, 4) = −p^{4} + p^{5}

(4, 6, 4, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  3 3  p^{5}

h(4, 6, 4, 6, 3) = p^{5}

(4, 6, 4, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  0 4  3 4  p^{5}

h(4, 6, 4, 6, 4) = p^{5}

(4, 6, 5, 2, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  0 0  −p^{3}

h(4, 6, 5, 2, 0) = −p^{3}

\begin{matrix}(4, 6, 5, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 2  1 1 & 0 \\ (4, 6, 5, 2, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  0 1 & 0 \end{matrix}

(4, 6, 5, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 2  1 2  0

(4, 6, 5, 2, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  0 2  −p^{3}(p − 1)

h(4, 6, 5, 2, 2) = p^{3} − p^{4}

(4, 6, 5, 2, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  0 3  −p^{4}

h(4, 6, 5, 2, 3) = −p^{4}

(4, 6, 5, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  0 0 0

\begin{matrix}(4, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 3  1 1 & 0 \\ (4, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 3  1 1 & 0 \\ (4, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 3  1 1 & 0 \\ (4, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  1 1 & 0 \\ (4, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  0 1 & 0 \end{matrix}

897

\begin{matrix}(4, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 3  1 2 & 0 \\ (4, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 3  1 2 & 0 \\ (4, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 3  1 2 & 0 \\ (4, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  1 2 & 0 \\ (4, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  0 2 & 0 \end{matrix}

898

\begin{matrix}(4, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 3  1 3 & 0 \\ (4, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 3  1 3 & 0 \\ (4, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 3  1 3 & 0 \\ (4, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  1 3 & 0 \\ (4, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  0 3 & 0 \end{matrix}

(4, 6, 5, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  0 4 0

(4, 6, 5, 4, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  0 0  p^{3}

h(4, 6, 5, 4, 0) = p^{3}

\begin{matrix}(4, 6, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 4  1 1 & 0 \\ (4, 6, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 4  1 1 & 0 \\ (4, 6, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  1 1 & 0 \\ (4, 6, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  1 1 & 0 \\ (4, 6, 5, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  0 1 & 0 \end{matrix}

900

(4, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 4  1 2  0

(4, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 3  2 2  0

(4, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 4  1 2  0

(4, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 3  2 2  0

(4, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  1 2  0

(4, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  2 2  −p^{4}(p − 1)

(4, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  1 2  0

(4, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  0 2  p^{3}(p − 1)

h(4, 6, 5, 4, 2) = −p^{3} + 2p^{4} − p^{5}

(4, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 4  1 3  0

(4, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 3  2 3  0

(4, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 4  1 3  0

(4, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 3  2 3  0

(4, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  1 3  0

(4, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 3  2 3  −p^{4}(p − 1)

(4, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  1 3  0

(4, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  0 3  0

h(4, 6, 5, 4, 3) = p^{4} − p^{5}

(4, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 4  1 4  0

(4, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  1 4  0

(4, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  1 4  0

(4, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  0 4  p^{4}(p − 1)

h(4, 6, 5, 4, 4) = −p^{4} + p^{5}

(4, 6, 5, 4, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  0 5  p^{5}

h(4, 6, 5, 4, 5) = p^{5}

\begin{matrix}(4, 6, 5, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  1 1 & 0 \\ (4, 6, 5, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  1 1 & 0 \end{matrix}

\begin{matrix}(4, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 4  2 2 & 0 \\ (4, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 4  2 2 & 0 \\ (4, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  1 2 & 0 \\ (4, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  2 2 & 0 \\ (4, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  2 2 & 0 \\ (4, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  1 2 & 0 \end{matrix}

904

\begin{matrix}(4, 6, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 4  2 3 & 0 \\ (4, 6, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 4  2 3 & 0 \\ (4, 6, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  1 3 & 0 \\ (4, 6, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  2 3 & 0 \\ (4, 6, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  2 3 & 0 \\ (4, 6, 5, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  1 3 & 0 \end{matrix}

905

\begin{matrix}(4, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 4  2 4 & 0 \\ (4, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 4  2 4 & 0 \\ (4, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  1 4 & 0 \\ (4, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  2 4 & 0 \\ (4, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  2 4 & 0 \\ (4, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  1 4 & 0 \end{matrix} \begin{matrix}(4, 6, 5, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  1 5 & 0 \\ (4, 6, 5, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  1 5 & 0 \end{matrix}

906

(4, 6, 5, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  2 2  0 ; (4, 6, 5, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  2 2  p^{4}(p − 1) ; h(4, 6, 5, 6, 2) = −p^{4} + p^{5} (4, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  1 4  3 3  0 ; (4, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  2 3  0 ; (4, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  3 3  0 ; (4, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  3 3  −p^{5}(p − 1) ; (4, 6, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  2 3  0 ; h(4, 6, 5, 6, 3) = p^{5} − p^{6}

907

(4, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  2 4  0

(4, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  1 4  3 4  0

(4, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 4  3 4  −p^{5}(p − 1)

(4, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  2 4  p^{4}(p − 1)^{2}

h(4, 6, 5, 6, 4) = p^{4} − p^{5}

(4, 6, 5, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  2  1 5  2 5  0

(4, 6, 5, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  2 5  p^{5}(p − 1)

h(4, 6, 5, 6, 5) = −p^{5} + p^{6}

(4, 6, 5, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  3 3  −p^{6}

h(4, 6, 5, 7, 3) = −p^{6}

(4, 6, 5, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  3 4 0

(4, 6, 5, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  0 5  3 5  p^{6}

h(4, 6, 5, 7, 5) = p^{6}

(4, 6, 6, 3, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  0 0  p^{3}

h(4, 6, 6, 3, 0) = p^{3}

\begin{matrix}(4, 6, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 3  1 1 & 0 \\ (4, 6, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 3  1 1 & 0 \\ (4, 6, 6, 3, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  0 1 & 0 \end{matrix}

(4, 6, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 3  1 2  0

(4, 6, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  0 2  p^{3}(p − 1)

h(4, 6, 6, 3, 2) = −p^{3} + p^{4}

\begin{matrix}(4, 6, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 3  1 3 & 0 \\ (4, 6, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 3  1 3 & 0 \\ (4, 6, 6, 3, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  0 3 & 0 \end{matrix}

(4, 6, 6, 3, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  0 4  −p^{4}

h(4, 6, 6, 3, 4) = −p^{4}

(4, 6, 6, 4, 0) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  0 0  p^{3}

h(4, 6, 6, 4, 0) = p^{3}

\begin{matrix}(4, 6, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 4  1 1 & 0 \\ (4, 6, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  1 1 & 0 \\ (4, 6, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  1 1 & 0 \\ (4, 6, 6, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  0 1 & 0 \end{matrix}

911

(4, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 3  2 2  0

(4, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 4  1 2  0

(4, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  2 3  2 2  −p^{5}(p − 1)

(4, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 3  2 2  0

(4, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  1 2  0

(4, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  1 2  0

(4, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  0 2  p^{3}(p − 1)

h(4, 6, 6, 4, 2) = −p^{3} + p^{4} + p^{5} − p^{6}

(4, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 3  2 3  0

(4, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 4  1 3  0

(4, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  2 3  2 3  −p^{5}(p − 1)

(4, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 3  2 3  0

(4, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  1 3  0

(4, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  1 3  0

(4, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  0 3  0

h(4, 6, 6, 4, 3) = p^{5} − p^{6}

(4, 6, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  1 4  0

(4, 6, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  1 4  0

(4, 6, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  0 4  p^{4}(p − 1)

h(4, 6, 6, 4, 4) = −p^{4} + p^{5}

(4, 6, 6, 4, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  0 5  p^{5}

h(4, 6, 6, 4, 5) = p^{5}

\begin{matrix}(4, 6, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  1 1 & 0 \\ (4, 6, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  1 1 & 0 \\ (4, 6, 6, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  1 1 & 0 \end{matrix}

(4, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 4  2 2  0

(4, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  1 2  0

(4, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  2 4  2 2  −p^{5}(p − 1)

(4, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  2 2  0

(4, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  1 2  0

(4, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  2 2  p^{4}(p − 1)

(4, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  1 2  0

h(4, 6, 6, 5, 2) = −p^{4} + 2p^{5} − p^{6}

\begin{matrix}(4, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 4  3  2 4  2 3 & 0 \\ (4, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 4  2 3 & 0 \\ (4, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  1 3 & 0 \\ (4, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  2 4  2 3 & 0 \\ (4, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  2 3 & 0 \\ (4, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  1 3 & 0 \\ (4, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  2 3 & 0 \\ (4, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  1 3 & 0 \end{matrix}

916

(4, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 4  2 4  0

(4, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  1 4  0

(4, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  2 4  2 4  p^{5}(p − 1)

(4, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  2 4  0

(4, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  1 4  0

(4, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  2 4  −p^{4}(p − 1)

(4, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  1 4  0

h(4, 6, 6, 5, 4) = p^{4} − 2p^{5} + p^{6}

\begin{matrix}(4, 6, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  1 5 & 0 \\ (4, 6, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  1 5 & 0 \\ (4, 6, 6, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  1 5 & 0 \end{matrix} (4, 6, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  2 2  0 ; (4, 6, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  2 2  0 ; (4, 6, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  2 2  p^{4}(p − 1) ; h(4, 6, 6, 6, 2) = −p^{4} + p^{5}

918

(4, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 4  3 3  0

(4, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  2 3  0

(4, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  2 4  3 3  p^{5}(p − 1)

(4, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  3 3  0

(4, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  2 3  0

(4, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  3 3  0

(4, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  2 3  0

h(4, 6, 6, 6, 3) = −p^{5} + p^{6}

(4, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 4  3 4  0

(4, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  2 4  0

(4, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 4  3  2 4  3 4  p^{5}(p − 1)

(4, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 4  3 4  0

(4, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  2 4  0

(4, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 4  3 4  0

(4, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  2 4  p^{4}(p − 1)^{2}

h(4, 6, 6, 6, 4) = p^{4} − 3p^{5} + 2p^{6}

(4, 6, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  2 5  0

(4, 6, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  2 5  p^{5}(p − 1)

h(4, 6, 6, 6, 5) = −p^{5} + p^{6}

\begin{matrix}(4, 6, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  3 3 & 0 \\ (4, 6, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  3 3 & 0 \\ (4, 6, 6, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  3 3 & 0 \end{matrix}

\begin{matrix}(4, 6, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  3 4 & 0 \\ (4, 6, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  3 4 & 0 \\ (4, 6, 6, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  3 4 & 0 \end{matrix}

\begin{matrix}(4, 6, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  1 5  3 5 & 0 \\ (4, 6, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  1 5  3 5 & 0 \\ (4, 6, 6, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  3 5 & 0 \end{matrix}

(4, 6, 6, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  4 4  −p^{6}

h(4, 6, 6, 8, 4) = −p^{6}

(4, 6, 6, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  0 5  4 5  −p^{6}

h(4, 6, 6, 8, 5) = −p^{6}

\begin{matrix}(4, 6, 7, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  1 1 & 0 \\ (4, 6, 7, 4, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  1 1 & 0 \end{matrix}

(4, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 3  2 2  0 ; (4, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  1 2  0 ; (4, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 3  2 2  −p^{5}(p − 1) ; (4, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  1 2  0 ; h(4, 6, 7, 4, 2) = p^{5} − p^{6} (4, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 3  2 3  0 ; (4, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  1 3  0 ; (4, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 3  2 3  −p^{5}(p − 1) ; (4, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  1 3  0 ; h(4, 6, 7, 4, 3) = p^{5} − p^{6}

923

\begin{matrix}(4, 6, 7, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  1 4 & 0 \\ (4, 6, 7, 4, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  1 4 & 0 \end{matrix} \begin{matrix}(4, 6, 7, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  1 1 & 0 \\ (4, 6, 7, 5, 1) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  1 1 & 0 \end{matrix}

924

\begin{matrix}(4, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 4  2 2 & 0 \\ (4, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  2 2 & 0 \\ (4, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  1 2 & 0 \\ (4, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 4  2 2 & 0 \\ (4, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  2 2 & 0 \\ (4, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  1 2 & 0 \end{matrix}

925

\begin{matrix}(4, 6, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 4  2 3 & 0 \\ (4, 6, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  2 3 & 0 \\ (4, 6, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  1 3 & 0 \\ (4, 6, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 4  2 3 & 0 \\ (4, 6, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  2 3 & 0 \\ (4, 6, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  1 3 & 0 \end{matrix}

926

\begin{matrix}(4, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 4  2 4 & 0 \\ (4, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  2 4 & 0 \\ (4, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  1 4 & 0 \\ (4, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 4  2 4 & 0 \\ (4, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  2 4 & 0 \\ (4, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  1 4 & 0 \end{matrix} \begin{matrix}(4, 6, 7, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  1 5 & 0 \\ (4, 6, 7, 5, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  1 5 & 0 \end{matrix}

927

(4, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  2 2  0

(4, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 5  2 2  p^{5}(p − 1)

(4, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  2 2  0

h(4, 6, 7, 6, 2) = −p^{5} + p^{6}

(4, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 5  2 3  0

(4, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  3 3  0

(4, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  2 3  0

(4, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 4  3 3  −p^{5}(p − 1)^{2}

(4, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 5  2 3  0

(4, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  3 3  0

(4, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  2 3  0

h(4, 6, 7, 6, 3) = −p^{5} + 2p^{6} − p^{7}

(4, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 4  3 4  0
(4, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 5  2 4  0
(4, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 4  3 4  0
(4, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  2 4  0
(4, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 4  3 4 −p^{5}(p − 1)^{2}
(4, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 5  2 4  p^{5}(p − 1)^{2}
(4, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 4  3 4  0
(4, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  2 4  0

cancel

(4, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 5  2 5  0 ; (4, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  2 5  0 ; (4, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 5  2 5  p^{6}(p − 1) ; (4, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  2 5  0 ; h(4, 6, 7, 6, 5) = −p^{6} + p^{7} (4, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 5  3 3  0 ; (4, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  3 3  0 ; (4, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 5  3 3  −p^{6}(p − 1) ; (4, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  3 3  0 ; h(4, 6, 7, 7, 3) = p^{6} − p^{7}

931

\begin{matrix}(4, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 5  3 4 & 0 \\ (4, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  3 4 & 0 \\ (4, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 5  3 4 & 0 \\ (4, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  3 4 & 0 \end{matrix} (4, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  3  2 5  3 5  0 ; (4, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  3 5  0 ; (4, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  3  2 5  3 5  p^{6}(p − 1) ; (4, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  3 5  0 ; h(4, 6, 7, 7, 5) = −p^{6} + p^{7}

932

\begin{matrix}(4, 6, 7, 8, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  4 4 & 0 \\ (4, 6, 7, 8, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  4 4 & 0 \end{matrix}

\begin{matrix}(4, 6, 7, 8, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  1 5  4 5 & 0 \\ (4, 6, 7, 8, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  1 5  4 5 & 0 \end{matrix}

(4, 6, 8, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 4  2 2  0

(4, 6, 8, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 4  2 2  p^{5}(p − 1)

h(4, 6, 8, 5, 2) = −p^{5} + p^{6}

\begin{matrix}(4, 6, 8, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 4  2 3 & 0 \\ (4, 6, 8, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 4  2 3 & 0 \end{matrix}

(4, 6, 8, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 4  2 4  −p^{5}(p − 1)

h(4, 6, 8, 5, 4) = p^{5} − p^{6}

(4, 6, 8, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  2 2  0

(4, 6, 8, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  2 2  p^{5}(p − 1)

h(4, 6, 8, 6, 2) = −p^{5} + p^{6}

\begin{matrix}(4, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 4  3 3 & 0 \\ (4, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  2 3 & 0 \\ (4, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 4  3 3 & 0 \\ (4, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  2 3 & 0 \end{matrix}

(4, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  2 4  0

(4, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 4  3 4  0

(4, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  2 4  p^{5}(p − 1)^{2}

h(4, 6, 8, 6, 4) = p^{5} − 2p^{6} + p^{7}

(4, 6, 8, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  2 5  0

(4, 6, 8, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  2 5  p^{6}(p − 1)

h(4, 6, 8, 6, 5) = −p^{6} + p^{7}

\begin{matrix}(4, 6, 8, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  3 3 & 0 \\ (4, 6, 8, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  3 3 & 0 \end{matrix}

\begin{matrix}(4, 6, 8, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  3 4 & 0 \\ (4, 6, 8, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  3 4 & 0 \end{matrix}

\begin{matrix}(4, 6, 8, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  3 5 & 0 \\ (4, 6, 8, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  3 5 & 0 \end{matrix}

(4, 6, 8, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  4 4  0

(4, 6, 8, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  4 4  −p^{6}(p − 1)

h(4, 6, 8, 8, 4) = p^{6} − p^{7}

(4, 6, 8, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  2  1 5  4  2 5  4 5  0

(4, 6, 8, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  2 5  4 5  −p^{6}(p − 1)

h(4, 6, 8, 8, 5) = p^{6} − p^{7}

h(4, 6, 9, 6, 3) = p^{7}

(4, 6, 9, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  3 4  3 4  p^{7}

h(4, 6, 9, 6, 4) = p^{7}

(4, 6, 9, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  3 5  3 3  p^{7}

h(4, 6, 9, 7, 3) = p^{7}

(4, 6, 9, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  3 5  3 4 0

(4, 6, 9, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  3 5  3 5  −p^{7}

h(4, 6, 9, 7, 5) = −p^{7}

(4, 6, 9, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  3 5  4 4  −p^{7}

h(4, 6, 9, 8, 4) = −p^{7}

(4, 6, 9, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  0 5  4  3 5  4 5  −p^{7}

h(4, 6, 9, 8, 5) = −p^{7}

(4, 7, 5, 3, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 3  1 1 0

(4, 7, 5, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 3  1 2 0

(4, 7, 5, 3, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 3  1 3 0

(4, 7, 5, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  1 1 0

\begin{matrix}(4, 7, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 3  2 2 & 0 \\ (4, 7, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(4, 7, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 3  2 3 & 0 \\ (4, 7, 5, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  1 3 & 0 \end{matrix}

(4, 7, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  1 4 0

(4, 7, 5, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  2 2 0

(4, 7, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  2 3 0

(4, 7, 5, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  2 4 0

(4, 7, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  3 3 0

(4, 7, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  1 4  3 4 0

(4, 7, 6, 3, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 3  1 1 0

(4, 7, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 3  1 2 0

(4, 7, 6, 3, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 3  1 3 0

(4, 7, 6, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  1 1 0

\begin{matrix}(4, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  2 3  2 2 & 0 \\ (4, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 3  2 2 & 0 \\ (4, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(4, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  2 3  2 3 & 0 \\ (4, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 3  2 3 & 0 \\ (4, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  1 3 & 0 \end{matrix}

(4, 7, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  1 4 0

(4, 7, 6, 5, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  1 1 0

\begin{matrix}(4, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  2 4  2 2 & 0 \\ (4, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  2 2 & 0 \\ (4, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  1 2 & 0 \end{matrix}

\begin{matrix}(4, 7, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  2 4  2 3 & 0 \\ (4, 7, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  2 3 & 0 \\ (4, 7, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  1 3 & 0 \end{matrix}

\begin{matrix}(4, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  2 4  2 4 & 0 \\ (4, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  2 4 & 0 \\ (4, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  1 4 & 0 \end{matrix}

(4, 7, 6, 5, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  1 5 0

(4, 7, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  2 2 0

\begin{matrix}(4, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  2 4  3 3 & 0 \\ (4, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  3 3 & 0 \\ (4, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  2 3 & 0 \end{matrix}

\begin{matrix}(4, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 4  3  2 4  3 4 & 0 \\ (4, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 4  3 4 & 0 \\ (4, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  2 4 & 0 \end{matrix}

(4, 7, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  2 5 0

(4, 7, 6, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  3 3 0

(4, 7, 6, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  3 4 0

(4, 7, 6, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  1 5  3 5 0

(4, 7, 7, 4, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  1 1 0

\begin{matrix}(4, 7, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 3  2 2 & 0 \\ (4, 7, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(4, 7, 7, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 3  2 3 & 0 \\ (4, 7, 7, 4, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  1 3 & 0 \end{matrix}

(4, 7, 7, 4, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  1 4 0

(4, 7, 7, 5, 1) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  1 1 0

\begin{matrix}(4, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 4  2 2 & 0 \\ (4, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  2 2 & 0 \\ (4, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  1 2 & 0 \end{matrix}

\begin{matrix}(4, 7, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 4  2 3 & 0 \\ (4, 7, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  2 3 & 0 \\ (4, 7, 7, 5, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  1 3 & 0 \end{matrix}

\begin{matrix}(4, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 4  2 4 & 0 \\ (4, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  2 4 & 0 \\ (4, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  1 4 & 0 \end{matrix}

(4, 7, 7, 5, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  1 5 0

\begin{matrix}(4, 7, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 5  2 2 & 0 \\ (4, 7, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  2 2 & 0 \end{matrix}

\begin{matrix}(4, 7, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 4  3 3 & 0 \\ (4, 7, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 5  2 3 & 0 \\ (4, 7, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  3 3 & 0 \\ (4, 7, 7, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  2 3 & 0 \end{matrix} \begin{matrix}(4, 7, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 4  3 4 & 0 \\ (4, 7, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 5  2 4 & 0 \\ (4, 7, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 4  3 4 & 0 \\ (4, 7, 7, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  2 4 & 0 \end{matrix}

946

\begin{matrix}(4, 7, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 5  2 5 & 0 \\ (4, 7, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  2 5 & 0 \end{matrix}

\begin{matrix}(4, 7, 7, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 5  3 3 & 0 \\ (4, 7, 7, 7, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  3 3 & 0 \end{matrix}

\begin{matrix}(4, 7, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 5  3 4 & 0 \\ (4, 7, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  3 4 & 0 \end{matrix}

\begin{matrix}(4, 7, 7, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  3  2 5  3 5 & 0 \\ (4, 7, 7, 7, 5) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  3 5 & 0 \end{matrix}

(4, 7, 7, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  4 4 0

(4, 7, 7, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  1 5  4 5 0

(4, 7, 8, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 4  2 2 0

(4, 7, 8, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 4  2 3 0

(4, 7, 8, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 4  2 4 0

(4, 7, 8, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  2 2 0

\begin{matrix}(4, 7, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 4  3 3 & 0 \\ (4, 7, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  2 3 & 0 \end{matrix}

\begin{matrix}(4, 7, 8, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 4  3 4 & 0 \\ (4, 7, 8, 6, 4) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  2 4 & 0 \end{matrix}

(4, 7, 8, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  2 5 0

(4, 7, 8, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  3 3 0

(4, 7, 8, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  3 4 0

(4, 7, 8, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  3 5 0

(4, 7, 8, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  4 4 0

(4, 7, 8, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  2 5  4 5 0

(4, 7, 9, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  3 4  3 3 0

(4, 7, 9, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  3 4  3 4 0

(4, 7, 9, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  3 5  3 3 0

(4, 7, 9, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  3 5  3 4 0

(4, 7, 9, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  3 5  3 5 0

(4, 7, 9, 8, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  3 5  4 4 0

(4, 7, 9, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  1 5  4  3 5  4 5 0

(4, 8, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 4  3  2 3  2 2  p^{6}

h(4, 8, 6, 4, 2) = p^{6}

(4, 8, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 4  3  2 3  2 3  p^{6}

h(4, 8, 6, 4, 3) = p^{6}

(4, 8, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 4  3  2 4  2 2  p^{6}

h(4, 8, 6, 5, 2) = p^{6}

(4, 8, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 4  3  2 4  2 3 0

(4, 8, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 4  3  2 4  2 4  −p^{6}

h(4, 8, 6, 5, 4) = −p^{6}

(4, 8, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 4  3  2 4  3 3  −p^{6}

h(4, 8, 6, 6, 3) = −p^{6}

(4, 8, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 4  3  2 4  3 4  −p^{6}

h(4, 8, 6, 6, 4) = −p^{6}

(4, 8, 7, 4, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 3  2 2  p^{6}

h(4, 8, 7, 4, 2) = p^{6}

(4, 8, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 3  2 3  p^{6}

h(4, 8, 7, 4, 3) = p^{6}

(4, 8, 7, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 4  2 2 0

(4, 8, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 4  2 3 0

(4, 8, 7, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 4  2 4 0

(4, 8, 7, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 5  2 2  −p^{6}

h(4, 8, 7, 6, 2) = −p^{6}

(4, 8, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 4  3 3  p^{6}(p − 1)

(4, 8, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 5  2 3  0

h(4, 8, 7, 6, 3) = −p^{6} + p^{7}

(4, 8, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 4  3 4  p^{6}(p − 1)

(4, 8, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 5  2 4 −p^{6}(p − 1)

cancel

(4, 8, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 5  2 5  −p^{7}

h(4, 8, 7, 6, 5) = −p^{7}

h(4, 8, 7, 7, 3) = p^{7}

(4, 8, 7, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 5  3 4 0

(4, 8, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  3  2 5  3 5  −p^{7}

h(4, 8, 7, 7, 5) = −p^{7}

(4, 8, 8, 5, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 4  2 2  −p^{6}

h(4, 8, 8, 5, 2) = −p^{6}

(4, 8, 8, 5, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 4  2 3 0

(4, 8, 8, 5, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 4  2 4  p^{6}

h(4, 8, 8, 5, 4) = p^{6}

(4, 8, 8, 6, 2) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 5  2 2  −p^{6}

h(4, 8, 8, 6, 2) = −p^{6}

\begin{matrix}(4, 8, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 4  3 3 & 0 \\ (4, 8, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 5  2 3 & 0 \end{matrix}

(4, 8, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 4  3 4  0

(4, 8, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 5  2 4  −p^{6}(p − 1)

h(4, 8, 8, 6, 4) = p^{6} − p^{7}

(4, 8, 8, 6, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 5  2 5  −p^{7}

h(4, 8, 8, 6, 5) = −p^{7}

(4, 8, 8, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 5  3 3 0

(4, 8, 8, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 5  3 4 0

(4, 8, 8, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 5  3 5 0

h(4, 8, 8, 8, 4) = p^{7}

(4, 8, 8, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  2 5  4 5  p^{7}

h(4, 8, 8, 8, 5) = p^{7}

(4, 8, 9, 6, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  3 4  3 3  −p^{7}

h(4, 8, 9, 6, 3) = −p^{7}

(4, 8, 9, 6, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  3 4  3 4  −p^{7}

h(4, 8, 9, 6, 4) = −p^{7}

(4, 8, 9, 7, 3) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  3 5  3 3  −p^{7}

h(4, 8, 9, 7, 3) = −p^{7}

(4, 8, 9, 7, 4) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  3 5  3 4 0

(4, 8, 9, 7, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  3 5  3 5  p^{7}

h(4, 8, 9, 7, 5) = p^{7}

h(4, 8, 9, 8, 4) = p^{7}

(4, 8, 9, 8, 5) 5  4  3  2  1  0 5  4  3  2  0 5  4  3  2 5  4  3 5  4 5  p^{7}

h(4, 8, 9, 8, 5) = p^{7}

(5, 4, 3, 2, 1) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 3  2  1 2  1 1  p^{4}

h(5, 4, 3, 2, 1) = p^{4}

(5, 4, 3, 2, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 3  2  1 2  1 2  p^{4}

h(5, 4, 3, 2, 2) = p^{4}

(5, 4, 3, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 3  2  1 3  1 1  p^{4}

h(5, 4, 3, 3, 1) = p^{4}

(5, 4, 3, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 3  2  1 3  1 2 0

(5, 4, 3, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 3  2  1 3  1 3  −p^{4}

h(5, 4, 3, 3, 3) = −p^{4}

h(5, 4, 3, 4, 2) = −p^{4}

(5, 4, 3, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 3  2  1 3  2 3  −p^{4}

h(5, 4, 3, 4, 3) = −p^{4}

(5, 4, 4, 2, 1) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 2  1 1  p^{4}

h(5, 4, 4, 2, 1) = p^{4}

(5, 4, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 2  1 2  p^{4}

h(5, 4, 4, 2, 2) = p^{4}

(5, 4, 4, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 3  1 1 0

(5, 4, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 3  1 2 0

(5, 4, 4, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 3  1 3 0

h(5, 4, 4, 4, 1) = −p^{4}

(5, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 3  2 2  p^{4}(p − 1)

(5, 4, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 4  1 2  0

h(5, 4, 4, 4, 2) = −p^{4} + p^{5}

(5, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 3  2 3  p^{4}(p − 1)

(5, 4, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 4  1 3 −p^{4}(p − 1)

cancel

(5, 4, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 4  1 4  −p^{5}

h(5, 4, 4, 4, 4) = −p^{5}

(5, 4, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 4  2 2  p^{5}

h(5, 4, 4, 5, 2) = p^{5}

(5, 4, 4, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  2  1 4  2 3 0

h(5, 4, 4, 5, 4) = −p^{5}

(5, 4, 5, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 3  1 1  −p^{4}

h(5, 4, 5, 3, 1) = −p^{4}

(5, 4, 5, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 3  1 2 0

(5, 4, 5, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 3  1 3  p^{4}

h(5, 4, 5, 3, 3) = p^{4}

(5, 4, 5, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  1 1  −p^{4}

h(5, 4, 5, 4, 1) = −p^{4}

\begin{matrix}(5, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 3  2 2 & 0 \\ (5, 4, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  1 2 & 0 \end{matrix}

(5, 4, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  1 3  −p^{4}(p − 1)

h(5, 4, 5, 4, 3) = p^{4} − p^{5}

(5, 4, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  1 4  −p^{5}

h(5, 4, 5, 4, 4) = −p^{5}

(5, 4, 5, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  2 2 0

(5, 4, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  2 3 0

(5, 4, 5, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  2 4 0

(5, 4, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  3 3  p^{5}

h(5, 4, 5, 6, 3) = p^{5}

(5, 4, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  1 4  3 4  p^{5}

h(5, 4, 5, 6, 4) = p^{5}

h(5, 4, 6, 4, 2) = −p^{5}

(5, 4, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  2 3  2 3  −p^{5}

h(5, 4, 6, 4, 3) = −p^{5}

(5, 4, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  2 4  2 2  −p^{5}

h(5, 4, 6, 5, 2) = −p^{5}

(5, 4, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  2 4  2 3 0

(5, 4, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  2 4  2 4  p^{5}

h(5, 4, 6, 5, 4) = p^{5}

(5, 4, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  2 4  3 3  p^{5}

h(5, 4, 6, 6, 3) = p^{5}

(5, 4, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 4  3  2  1 4  3  2 4  3 4  p^{5}

h(5, 4, 6, 6, 4) = p^{5}

h(5, 5, 3, 2, 1) = p^{4}

(5, 5, 3, 2, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 3  2  1 2  1 2  p^{4}

h(5, 5, 3, 2, 2) = p^{4}

(5, 5, 3, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 3  2  1 3  1 1  p^{4}

h(5, 5, 3, 3, 1) = p^{4}

(5, 5, 3, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 3  2  1 3  1 2 0

(5, 5, 3, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 3  2  1 3  1 3  −p^{4}

h(5, 5, 3, 3, 3) = −p^{4}

(5, 5, 3, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 3  2  1 3  2 2  −p^{4}

h(5, 5, 3, 4, 2) = −p^{4}

(5, 5, 3, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 3  2  1 3  2 3  −p^{4}

h(5, 5, 3, 4, 3) = −p^{4}

(5, 5, 4, 2, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 2  1 1 0

(5, 5, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 2  1 2 0

(5, 5, 4, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 3  1 1 0

(5, 5, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 3  1 2 0

(5, 5, 4, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 3  1 3 0

(5, 5, 4, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 4  1 1 0

\begin{matrix}(5, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 3  2 2 & 0 \\ (5, 5, 4, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(5, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 3  2 3 & 0 \\ (5, 5, 4, 4, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 4  1 3 & 0 \end{matrix}

(5, 5, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 4  1 4 0

(5, 5, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 4  2 2 0

(5, 5, 4, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 4  2 3 0

(5, 5, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  2  1 4  2 4 0

(5, 5, 5, 2, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 2  1 1  −p^{4}

h(5, 5, 5, 2, 1) = −p^{4}

(5, 5, 5, 2, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 2  1 2  −p^{4}

h(5, 5, 5, 2, 2) = −p^{4}

(5, 5, 5, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 3  1 1  p^{4}(p − 1)
(5, 5, 5, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 3  1 1  0

h(5, 5, 5, 3, 1) = −p^{4} + p^{5}

\begin{matrix}(5, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 3  1 2 & 0 \\ (5, 5, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 3  1 2 & 0 \end{matrix}
(5, 5, 5, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 3  1 3  −p^{4}(p − 1)
(5, 5, 5, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 3  1 3  0

h(5, 5, 5, 3, 3) = p^{4} − p^{5}

(5, 5, 5, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 4  1 1  p^{4}(p − 1)
(5, 5, 5, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 4  1 1 −p^{4}(p − 1)

cancel

(5, 5, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 3  2 2  0 ; (5, 5, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 4  1 2  0 ; (5, 5, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 3  2 2  −p^{4}(p − 1) ; (5, 5, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 4  1 2  0 ; h(5, 5, 5, 4, 2) = p^{4} − p^{5} (5, 5, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 3  2 3  0 ; (5, 5, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 4  1 3  p^{4}(p − 1)^{2} ; (5, 5, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 3  2 3  −p^{4}(p − 1) ; (5, 5, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 4  1 3  −p^{4}(p − 1)^{2} ; h(5, 5, 5, 4, 3) = p^{4} − p^{5}

966

(5, 5, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 4  1 4 −p^{5}(p − 1)

cancel

(5, 5, 5, 5, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  1 1  −p^{5}

h(5, 5, 5, 5, 1) = −p^{5}

\begin{matrix}(5, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 4  2 2 & 0 \\ (5, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 4  2 2 & 0 \\ (5, 5, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  1 2 & 0 \end{matrix}

(5, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 4  2 3  0

(5, 5, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  1 3  −p^{5}(p − 1)

h(5, 5, 5, 5, 3) = p^{5} − p^{6}

\begin{matrix}(5, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 4  2 4 & 0 \\ (5, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 4  2 4 & 0 \\ (5, 5, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  1 4 & 0 \end{matrix}

(5, 5, 5, 5, 5) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  1 5  p^{6}

h(5, 5, 5, 5, 5) = p^{6}

(5, 5, 5, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  2 2  p^{5}

h(5, 5, 5, 6, 2) = p^{5}

(5, 5, 5, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  2 3  0

h(5, 5, 5, 6, 3) = p^{5} − p^{6}

(5, 5, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  1 4  3 4 −p^{5}(p − 1)

(5, 5, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  2 4  p^{5}(p − 1)

cancel

(5, 5, 5, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  2  1 5  2 5  p^{6}

h(5, 5, 5, 6, 5) = p^{6}

(5, 5, 6, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 3  1 1  p^{5}

h(5, 5, 6, 3, 1) = p^{5}

(5, 5, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 3  1 2 0

(5, 5, 6, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 3  1 3  −p^{5}

h(5, 5, 6, 3, 3) = −p^{5}

(5, 5, 6, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  1 1 0

\begin{matrix}(5, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  2 3  2 2 & 0 \\ (5, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 3  2 2 & 0 \\ (5, 5, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(5, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  2 3  2 3 & 0 \\ (5, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 3  2 3 & 0 \\ (5, 5, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  1 3 & 0 \end{matrix}

(5, 5, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  1 4 0

(5, 5, 6, 5, 1) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  1 1  −p^{5}

h(5, 5, 6, 5, 1) = −p^{5}

\begin{matrix}(5, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  2 4  2 2 & 0 \\ (5, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  2 2 & 0 \\ (5, 5, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  1 2 & 0 \end{matrix}

(5, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  2 4  2 3  0

(5, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  2 3  0

(5, 5, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  1 3  −p^{5}(p − 1)

h(5, 5, 6, 5, 3) = p^{5} − p^{6}

\begin{matrix}(5, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  2 4  2 4 & 0 \\ (5, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  2 4 & 0 \\ (5, 5, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  1 4 & 0 \end{matrix}

h(5, 5, 6, 5, 5) = p^{6}

(5, 5, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  2 2 0

\begin{matrix}(5, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  2 4  3 3 & 0 \\ (5, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  3 3 & 0 \\ (5, 5, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  2 3 & 0 \end{matrix}

\begin{matrix}(5, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 4  3  2 4  3 4 & 0 \\ (5, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 4  3 4 & 0 \\ (5, 5, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  2 4 & 0 \end{matrix}

(5, 5, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  2 5 0

h(5, 5, 6, 7, 3) = p^{6}

(5, 5, 6, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  3 4 0

(5, 5, 6, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  1 5  3 5  −p^{6}

h(5, 5, 6, 7, 5) = −p^{6}

(5, 5, 7, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 3  2 2  p^{5}

h(5, 5, 7, 4, 2) = p^{5}

(5, 5, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 3  2 3  p^{5}

h(5, 5, 7, 4, 3) = p^{5}

(5, 5, 7, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 4  2 2 0

(5, 5, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 4  2 3 0

(5, 5, 7, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 4  2 4 0

h(5, 5, 7, 6, 2) = −p^{5}

(5, 5, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 4  3 3  p^{5}(p − 1)

(5, 5, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 5  2 3  0

h(5, 5, 7, 6, 3) = −p^{5} + p^{6}

(5, 5, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 4  3 4  p^{5}(p − 1)

(5, 5, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 5  2 4 −p^{5}(p − 1)

cancel

(5, 5, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 5  2 5  −p^{6}

h(5, 5, 7, 6, 5) = −p^{6}

(5, 5, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 5  3 3  p^{6}

h(5, 5, 7, 7, 3) = p^{6}

(5, 5, 7, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  3  2  1 5  3  2 5  3 4 0

h(5, 5, 7, 7, 5) = −p^{6}

(5, 6, 4, 2, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 2  1 1  −p^{4}

h(5, 6, 4, 2, 1) = −p^{4}

(5, 6, 4, 2, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 2  1 2  −p^{4}

h(5, 6, 4, 2, 2) = −p^{4}

(5, 6, 4, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 3  1 1 0

(5, 6, 4, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 3  1 2 0

(5, 6, 4, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 3  1 3 0

(5, 6, 4, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 4  1 1  p^{4}

h(5, 6, 4, 4, 1) = p^{4}

(5, 6, 4, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 4  1 2  0

h(5, 6, 4, 4, 2) = p^{4} − p^{5}

(5, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 3  2 3 −p^{4}(p − 1)

(5, 6, 4, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 4  1 3  p^{4}(p − 1)

cancel

(5, 6, 4, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 4  1 4  p^{5}

h(5, 6, 4, 4, 4) = p^{5}

(5, 6, 4, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 4  2 2  −p^{5}

h(5, 6, 4, 5, 2) = −p^{5}

(5, 6, 4, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 4  2 3 0

(5, 6, 4, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  2  1 4  2 4  p^{5}

h(5, 6, 4, 5, 4) = p^{5}

h(5, 6, 5, 2, 1) = −p^{4}

(5, 6, 5, 2, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 2  1 2  −p^{4}

h(5, 6, 5, 2, 2) = −p^{4}

\begin{matrix}(5, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 3  1 1 & 0 \\ (5, 6, 5, 3, 1) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 3  1 1 & 0 \end{matrix}

\begin{matrix}(5, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 3  1 2 & 0 \\ (5, 6, 5, 3, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 3  1 2 & 0 \end{matrix}

\begin{matrix}(5, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 3  1 3 & 0 \\ (5, 6, 5, 3, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 3  1 3 & 0 \end{matrix}

(5, 6, 5, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  1 1  0 ; (5, 6, 5, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 4  1 1  −p^{4}(p − 1) ; h(5, 6, 5, 4, 1) = p^{4} − p^{5} (5, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 3  2 2  0 ; (5, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  1 2  0 ; (5, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 3  2 2  −p^{4}(p − 1) ; (5, 6, 5, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 4  1 2  0 ; h(5, 6, 5, 4, 2) = p^{4} − p^{5}

978

(5, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  1 3  0

(5, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 3  2 3  −p^{4}(p − 1)

(5, 6, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 4  1 3  −p^{4}(p − 1)^{2}

h(5, 6, 5, 4, 3) = p^{5} − p^{6}

(5, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  1 4  0

(5, 6, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 4  1 4  −p^{5}(p − 1)

h(5, 6, 5, 4, 4) = p^{5} − p^{6}

(5, 6, 5, 5, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 5  1 1  −p^{5}

h(5, 6, 5, 5, 1) = −p^{5}

\begin{matrix}(5, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  2 2 & 0 \\ (5, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 4  2 2 & 0 \\ (5, 6, 5, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 5  1 2 & 0 \end{matrix}

(5, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  2 3  0

(5, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 4  2 3  0

(5, 6, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 5  1 3  −p^{5}(p − 1)

h(5, 6, 5, 5, 3) = p^{5} − p^{6}

\begin{matrix}(5, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  2 4 & 0 \\ (5, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 4  2 4 & 0 \\ (5, 6, 5, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 5  1 4 & 0 \end{matrix}

h(5, 6, 5, 5, 5) = p^{6}

(5, 6, 5, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 5  2 2  p^{5}

h(5, 6, 5, 6, 2) = p^{5}

\begin{matrix}(5, 6, 5, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  3 3 & 0 \\ (5, 6, 5, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 5  2 3 & 0 \end{matrix}

(5, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  1 4  3 4  0

(5, 6, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 5  2 4  p^{5}(p − 1)

h(5, 6, 5, 6, 4) = −p^{5} + p^{6}

(5, 6, 5, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  2  1 5  2 5  p^{6}

h(5, 6, 5, 6, 5) = p^{6}

(5, 6, 6, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 3  1 1 0

(5, 6, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 3  1 2 0

(5, 6, 6, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 3  1 3 0

(5, 6, 6, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  1 1 0

(5, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  2 3  2 2  −p^{5}(p − 1)

(5, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 3  2 2  0

(5, 6, 6, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  1 2  0

h(5, 6, 6, 4, 2) = p^{5} − p^{6}

(5, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 3  2 3  0

(5, 6, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  1 3  0

h(5, 6, 6, 4, 3) = p^{5} − p^{6}

(5, 6, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  1 4 0

(5, 6, 6, 5, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  1 1 0

(5, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  2 4  2 2  −p^{5}(p − 1)

(5, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  2 2  0

(5, 6, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  1 2  0

h(5, 6, 6, 5, 2) = p^{5} − p^{6}

\begin{matrix}(5, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  2 4  2 3 & 0 \\ (5, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  2 3 & 0 \\ (5, 6, 6, 5, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  1 3 & 0 \end{matrix}

(5, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  2 4  2 4  p^{5}(p − 1)

(5, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  2 4  0

(5, 6, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  1 4  0

h(5, 6, 6, 5, 4) = −p^{5} + p^{6}

(5, 6, 6, 5, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  1 5 0

(5, 6, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  2 2 0

(5, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  3 3  0

(5, 6, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  2 3  0

h(5, 6, 6, 6, 3) = −p^{5} + p^{6}

(5, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 4  3  2 4  3 4  p^{5}(p − 1)

(5, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 4  3 4  0

(5, 6, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  2 4  0

h(5, 6, 6, 6, 4) = −p^{5} + p^{6}

(5, 6, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  2 5 0

(5, 6, 6, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  3 3 0

(5, 6, 6, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  3 4 0

(5, 6, 6, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  1 5  3 5 0

(5, 6, 7, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  1 1  p^{5}

h(5, 6, 7, 4, 1) = p^{5}

(5, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 3  2 2  −p^{5}(p − 1)

(5, 6, 7, 4, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  1 2  0

h(5, 6, 7, 4, 2) = p^{5} − p^{6}

(5, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 3  2 3 −p^{5}(p − 1)

(5, 6, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  1 3  p^{5}(p − 1)

cancel

(5, 6, 7, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  1 4  p^{6}

h(5, 6, 7, 4, 4) = p^{6}

h(5, 6, 7, 5, 1) = p^{5}

\begin{matrix}(5, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 4  2 2 & 0 \\ (5, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  2 2 & 0 \\ (5, 6, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  1 2 & 0 \end{matrix}

(5, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 4  2 3  0

(5, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  2 3  0

(5, 6, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  1 3  p^{5}(p − 1)

h(5, 6, 7, 5, 3) = −p^{5} + p^{6}

\begin{matrix}(5, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 4  2 4 & 0 \\ (5, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  2 4 & 0 \\ (5, 6, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  1 4 & 0 \end{matrix}

(5, 6, 7, 5, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  1 5  −p^{6}

h(5, 6, 7, 5, 5) = −p^{6}

(5, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 5  2 2  p^{5}(p − 1)

(5, 6, 7, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  2 2  0

h(5, 6, 7, 6, 2) = −p^{5} + p^{6}

(5, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 4  3 3  −p^{5}(p − 1)^{2} ; (5, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 5  2 3  0 ; (5, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  3 3  p^{6}(p − 1) ; (5, 6, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  2 3  0 ; h(5, 6, 7, 6, 3) = −p^{5} + p^{6} (5, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 4  3 4  −p^{5}(p − 1)^{2} ; (5, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 5  2 4  p^{5}(p − 1)^{2} ; (5, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 4  3 4  p^{6}(p − 1) ; (5, 6, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  2 4  0 ; h(5, 6, 7, 6, 4) = −p^{6} + p^{7}

989

(5, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 5  2 5  p^{6}(p − 1)
(5, 6, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  2 5  0

h(5, 6, 7, 6, 5) = −p^{6} + p^{7}

(5, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 5  3 3 −p^{6}(p − 1)
(5, 6, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  3 3  p^{6}(p − 1)

cancel

\begin{matrix}(5, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 5  3 4 & 0 \\ (5, 6, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  3 4 & 0 \end{matrix}
(5, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  3  2 5  3 5  p^{6}(p − 1)
(5, 6, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  3 5 −p^{6}(p − 1)

cancel

h(5, 6, 7, 8, 4) = −p^{7}

(5, 6, 7, 8, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  1 5  4 5  −p^{7}

h(5, 6, 7, 8, 5) = −p^{7}

(5, 6, 8, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 4  2 2  p^{6}

h(5, 6, 8, 5, 2) = p^{6}

(5, 6, 8, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 4  2 3 0

(5, 6, 8, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 4  2 4  −p^{6}

h(5, 6, 8, 5, 4) = −p^{6}

(5, 6, 8, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 5  2 2  p^{6}

h(5, 6, 8, 6, 2) = p^{6}

\begin{matrix}(5, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 4  3 3 & 0 \\ (5, 6, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 5  2 3 & 0 \end{matrix}

(5, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 4  3 4  0

(5, 6, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 5  2 4  p^{6}(p − 1)

h(5, 6, 8, 6, 4) = −p^{6} + p^{7}

(5, 6, 8, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 5  2 5  p^{7}

h(5, 6, 8, 6, 5) = p^{7}

(5, 6, 8, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 5  3 3 0

(5, 6, 8, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 5  3 4 0

(5, 6, 8, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 5  3 5 0

h(5, 6, 8, 8, 4) = −p^{7}

(5, 6, 8, 8, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  2  1 5  4  2 5  4 5  −p^{7}

h(5, 6, 8, 8, 5) = −p^{7}

(5, 7, 5, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 3  1 1  −p^{5}

h(5, 7, 5, 3, 1) = −p^{5}

(5, 7, 5, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 3  1 2 0

(5, 7, 5, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 3  1 3  p^{5}

h(5, 7, 5, 3, 3) = p^{5}

(5, 7, 5, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 4  1 1  −p^{5}

h(5, 7, 5, 4, 1) = −p^{5}

\begin{matrix}(5, 7, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 3  2 2 & 0 \\ (5, 7, 5, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 4  1 2 & 0 \end{matrix}

(5, 7, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 3  2 3  0

(5, 7, 5, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 4  1 3  −p^{5}(p − 1)

h(5, 7, 5, 4, 3) = p^{5} − p^{6}

(5, 7, 5, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 4  1 4  −p^{6}

h(5, 7, 5, 4, 4) = −p^{6}

(5, 7, 5, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 4  2 2 0

(5, 7, 5, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 4  2 3 0

(5, 7, 5, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 4  2 4 0

h(5, 7, 5, 6, 3) = p^{6}

(5, 7, 5, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  1 4  3 4  p^{6}

h(5, 7, 5, 6, 4) = p^{6}

(5, 7, 6, 3, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 3  1 1  −p^{5}

h(5, 7, 6, 3, 1) = −p^{5}

(5, 7, 6, 3, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 3  1 2 0

(5, 7, 6, 3, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 3  1 3  p^{5}

h(5, 7, 6, 3, 3) = p^{5}

(5, 7, 6, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  1 1 0

\begin{matrix}(5, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  2 3  2 2 & 0 \\ (5, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 3  2 2 & 0 \\ (5, 7, 6, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  1 2 & 0 \end{matrix}

\begin{matrix}(5, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  2 3  2 3 & 0 \\ (5, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 3  2 3 & 0 \\ (5, 7, 6, 4, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  1 3 & 0 \end{matrix}

(5, 7, 6, 4, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  1 4 0

(5, 7, 6, 5, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  1 1  p^{5}

h(5, 7, 6, 5, 1) = p^{5}

\begin{matrix}(5, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  2 4  2 2 & 0 \\ (5, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  2 2 & 0 \\ (5, 7, 6, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  1 2 & 0 \end{matrix}

(5, 7, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  2 4  2 3  0

(5, 7, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  2 3  0

(5, 7, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  1 3  p^{5}(p − 1)

h(5, 7, 6, 5, 3) = −p^{5} + p^{6}

\begin{matrix}(5, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  2 4  2 4 & 0 \\ (5, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  2 4 & 0 \\ (5, 7, 6, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  1 4 & 0 \end{matrix}

h(5, 7, 6, 5, 5) = −p^{6}

(5, 7, 6, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  2 2 0

\begin{matrix}(5, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  2 4  3 3 & 0 \\ (5, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  3 3 & 0 \\ (5, 7, 6, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  2 3 & 0 \end{matrix}

\begin{matrix}(5, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 4  3  2 4  3 4 & 0 \\ (5, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 4  3 4 & 0 \\ (5, 7, 6, 6, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  2 4 & 0 \end{matrix}

(5, 7, 6, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  2 5 0

h(5, 7, 6, 7, 3) = −p^{6}

(5, 7, 6, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  3 4 0

(5, 7, 6, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  1 5  3 5  p^{6}

h(5, 7, 6, 7, 5) = p^{6}

(5, 7, 7, 4, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 4  1 1  p^{5}

h(5, 7, 7, 4, 1) = p^{5}

\begin{matrix}(5, 7, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 3  2 2 & 0 \\ (5, 7, 7, 4, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 4  1 2 & 0 \end{matrix}

(5, 7, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 3  2 3  0

(5, 7, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 4  1 3  p^{5}(p − 1)

h(5, 7, 7, 4, 3) = −p^{5} + p^{6}

h(5, 7, 7, 4, 4) = p^{6}

(5, 7, 7, 5, 1) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  1 1  p^{5}

h(5, 7, 7, 5, 1) = p^{5}

\begin{matrix}(5, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 4  2 2 & 0 \\ (5, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 4  2 2 & 0 \\ (5, 7, 7, 5, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  1 2 & 0 \end{matrix}

(5, 7, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 4  2 3  0

(5, 7, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 4  2 3  0

(5, 7, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  1 3  p^{5}(p − 1)

h(5, 7, 7, 5, 3) = −p^{5} + p^{6}

\begin{matrix}(5, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 4  2 4 & 0 \\ (5, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 4  2 4 & 0 \\ (5, 7, 7, 5, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  1 4 & 0 \end{matrix}

(5, 7, 7, 5, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  1 5  −p^{6}

h(5, 7, 7, 5, 5) = −p^{6}

\begin{matrix}(5, 7, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 5  2 2 & 0 \\ (5, 7, 7, 6, 2) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  2 2 & 0 \end{matrix}

(5, 7, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 4  3 3  0 ; (5, 7, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 5  2 3  0 ; (5, 7, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 4  3 3  p^{6}(p − 1) ; (5, 7, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  2 3  0 ; h(5, 7, 7, 6, 3) = −p^{6} + p^{7} (5, 7, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 4  3 4  0 ; (5, 7, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 5  2 4  0 ; (5, 7, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 4  3 4  p^{6}(p − 1) ; (5, 7, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  2 4  0 ; h(5, 7, 7, 6, 4) = −p^{6} + p^{7}

1002

\begin{matrix}(5, 7, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 5  2 5 & 0 \\ (5, 7, 7, 6, 5) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  2 5 & 0 \end{matrix}

(5, 7, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 5  3 3  0

(5, 7, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  3 3  p^{6}(p − 1)

h(5, 7, 7, 7, 3) = −p^{6} + p^{7}

\begin{matrix}(5, 7, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 5  3 4 & 0 \\ (5, 7, 7, 7, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  3 4 & 0 \end{matrix}

(5, 7, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  3  2 5  3 5  0

(5, 7, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  3 5  −p^{6}(p − 1)

h(5, 7, 7, 7, 5) = p^{6} − p^{7}

h(5, 7, 7, 8, 4) = −p^{7}

(5, 7, 7, 8, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  1 5  4 5  −p^{7}

h(5, 7, 7, 8, 5) = −p^{7}

(5, 7, 8, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 4  2 2 0

(5, 7, 8, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 4  2 3 0

(5, 7, 8, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 4  2 4 0

(5, 7, 8, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  2 2 0

\begin{matrix}(5, 7, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 4  3 3 & 0 \\ (5, 7, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  2 3 & 0 \end{matrix}

\begin{matrix}(5, 7, 8, 6, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 4  3 4 & 0 \\ (5, 7, 8, 6, 4) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  2 4 & 0 \end{matrix}

(5, 7, 8, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  2 5 0

(5, 7, 8, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  3 3 0

(5, 7, 8, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  3 4 0

(5, 7, 8, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  3 5 0

(5, 7, 8, 8, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  4 4 0

(5, 7, 8, 8, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  2 5  4 5 0

h(5, 7, 9, 6, 3) = −p^{7}

(5, 7, 9, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  3 4  3 4  −p^{7}

h(5, 7, 9, 6, 4) = −p^{7}

(5, 7, 9, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  3 5  3 3  −p^{7}

h(5, 7, 9, 7, 3) = −p^{7}

(5, 7, 9, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  3 5  3 4 0

(5, 7, 9, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  3 5  3 5  p^{7}

h(5, 7, 9, 7, 5) = p^{7}

(5, 7, 9, 8, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  3 5  4 4  p^{7}

h(5, 7, 9, 8, 4) = p^{7}

(5, 7, 9, 8, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  1 5  4  3 5  4 5  p^{7}

h(5, 7, 9, 8, 5) = p^{7}

h(5, 8, 6, 4, 2) = p^{6}

(5, 8, 6, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 4  3  2 3  2 3  p^{6}

h(5, 8, 6, 4, 3) = p^{6}

(5, 8, 6, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 4  3  2 4  2 2  p^{6}

h(5, 8, 6, 5, 2) = p^{6}

(5, 8, 6, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 4  3  2 4  2 3 0

(5, 8, 6, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 4  3  2 4  2 4  −p^{6}

h(5, 8, 6, 5, 4) = −p^{6}

(5, 8, 6, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 4  3  2 4  3 3  −p^{6}

h(5, 8, 6, 6, 3) = −p^{6}

(5, 8, 6, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 4  3  2 4  3 4  −p^{6}

h(5, 8, 6, 6, 4) = −p^{6}

h(5, 8, 7, 4, 2) = p^{6}

(5, 8, 7, 4, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 3  2 3  p^{6}

h(5, 8, 7, 4, 3) = p^{6}

(5, 8, 7, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 4  2 2 0

(5, 8, 7, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 4  2 3 0

(5, 8, 7, 5, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 4  2 4 0

(5, 8, 7, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 5  2 2  −p^{6}

h(5, 8, 7, 6, 2) = −p^{6}

(5, 8, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 4  3 3  p^{6}(p − 1)

(5, 8, 7, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 5  2 3  0

h(5, 8, 7, 6, 3) = −p^{6} + p^{7}

(5, 8, 7, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 5  2 4 −p^{6}(p − 1)

cancel

(5, 8, 7, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 5  2 5  −p^{7}

h(5, 8, 7, 6, 5) = −p^{7}

(5, 8, 7, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 5  3 3  p^{7}

h(5, 8, 7, 7, 3) = p^{7}

(5, 8, 7, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 5  3 4 0

(5, 8, 7, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  3  2 5  3 5  −p^{7}

h(5, 8, 7, 7, 5) = −p^{7}

(5, 8, 8, 5, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 4  2 2  −p^{6}

h(5, 8, 8, 5, 2) = −p^{6}

(5, 8, 8, 5, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 4  2 3 0

h(5, 8, 8, 5, 4) = p^{6}

(5, 8, 8, 6, 2) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  2 2  −p^{6}

h(5, 8, 8, 6, 2) = −p^{6}

\begin{matrix}(5, 8, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 4  3 3 & 0 \\ (5, 8, 8, 6, 3) & 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  2 3 & 0 \end{matrix}

(5, 8, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 4  3 4  0

(5, 8, 8, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  2 4  −p^{6}(p − 1)

h(5, 8, 8, 6, 4) = p^{6} − p^{7}

(5, 8, 8, 6, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  2 5  −p^{7}

h(5, 8, 8, 6, 5) = −p^{7}

(5, 8, 8, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  3 3 0

(5, 8, 8, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  3 4 0

(5, 8, 8, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  3 5 0

(5, 8, 8, 8, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  4 4  p^{7}

h(5, 8, 8, 8, 4) = p^{7}

(5, 8, 8, 8, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  2 5  4 5  p^{7}

h(5, 8, 8, 8, 5) = p^{7}

(5, 8, 9, 6, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  3 4  3 3  −p^{7}

h(5, 8, 9, 6, 3) = −p^{7}

(5, 8, 9, 6, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  3 4  3 4  −p^{7}

h(5, 8, 9, 6, 4) = −p^{7}

(5, 8, 9, 7, 3) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  3 5  3 3  −p^{7}

h(5, 8, 9, 7, 3) = −p^{7}

(5, 8, 9, 7, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  3 5  3 4 0

(5, 8, 9, 7, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  3 5  3 5  p^{7}

h(5, 8, 9, 7, 5) = p^{7}

(5, 8, 9, 8, 4) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  3 5  4 4  p^{7}

h(5, 8, 9, 8, 4) = p^{7}

(5, 8, 9, 8, 5) 5  4  3  2  1  0 5  4  3  2  1 5  4  3  2 5  4  3 5  4 5  p^{7}

h(5, 8, 9, 8, 5) = p^{7}

This completes the proof of the theorem.

References

[1] B. Brubaker, D. Bump, S. Friedberg, and J. Hoffstein. Weyl group multiple Dirichlet series III: Eisenstein series and twisted unstable A_{2}. Preprint,

available at http://sporadic.stanford.edu/bump/wmd3.ps.

[2] G. Chinta. Mean values of biquadratic zeta functions. Invent. Math., 160(1):145–163, 2005.