Subset Species¶
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class
sage.combinat.species.subset_species.
SubsetSpecies
(min=None, max=None, weight=None)¶ Bases:
sage.combinat.species.species.GenericCombinatorialSpecies
,sage.structure.unique_representation.UniqueRepresentation
Return the species of subsets.
EXAMPLES:
sage: S = species.SubsetSpecies() sage: S.generating_series().coefficients(5) [1, 2, 2, 4/3, 2/3] sage: S.isotype_generating_series().coefficients(5) [1, 2, 3, 4, 5] sage: S = species.SubsetSpecies() sage: c = S.generating_series().coefficients(3) sage: S._check() True sage: S == loads(dumps(S)) True
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class
sage.combinat.species.subset_species.
SubsetSpeciesStructure
(parent, labels, list)¶ Bases:
sage.combinat.species.structure.GenericSpeciesStructure
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automorphism_group
()¶ Return the group of permutations whose action on this subset leave it fixed.
EXAMPLES:
sage: F = species.SubsetSpecies() sage: a = F.structures([1,2,3,4])[6]; a {1, 3} sage: a.automorphism_group() Permutation Group with generators [(2,4), (1,3)]
sage: [a.transport(g) for g in a.automorphism_group()] [{1, 3}, {1, 3}, {1, 3}, {1, 3}]
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canonical_label
()¶ Return the canonical label of
self
.EXAMPLES:
sage: P = species.SubsetSpecies() sage: S = P.structures(["a", "b", "c"]) sage: [s.canonical_label() for s in S] [{}, {'a'}, {'a'}, {'a'}, {'a', 'b'}, {'a', 'b'}, {'a', 'b'}, {'a', 'b', 'c'}]
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complement
()¶ Return the complement of
self
.EXAMPLES:
sage: F = species.SubsetSpecies() sage: a = F.structures(["a", "b", "c"])[5]; a {'a', 'c'} sage: a.complement() {'b'}
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label_subset
()¶ Return a subset of the labels that “appear” in this structure.
EXAMPLES:
sage: P = species.SubsetSpecies() sage: S = P.structures(["a", "b", "c"]) sage: [s.label_subset() for s in S] [[], ['a'], ['b'], ['c'], ['a', 'b'], ['a', 'c'], ['b', 'c'], ['a', 'b', 'c']]
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transport
(perm)¶ Return the transport of this subset along the permutation perm.
EXAMPLES:
sage: F = species.SubsetSpecies() sage: a = F.structures(["a", "b", "c"])[5]; a {'a', 'c'} sage: p = PermutationGroupElement((1,2)) sage: a.transport(p) {'b', 'c'} sage: p = PermutationGroupElement((1,3)) sage: a.transport(p) {'a', 'c'}
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sage.combinat.species.subset_species.
SubsetSpecies_class
¶