Permutation species¶
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class
sage.combinat.species.permutation_species.
PermutationSpecies
(min=None, max=None, weight=None)¶ Bases:
sage.combinat.species.species.GenericCombinatorialSpecies
,sage.structure.unique_representation.UniqueRepresentation
Returns the species of permutations.
EXAMPLES:
sage: P = species.PermutationSpecies() sage: P.generating_series().coefficients(5) [1, 1, 1, 1, 1] sage: P.isotype_generating_series().coefficients(5) [1, 1, 2, 3, 5] sage: P = species.PermutationSpecies() sage: c = P.generating_series().coefficients(3) sage: P._check() True sage: P == loads(dumps(P)) True
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class
sage.combinat.species.permutation_species.
PermutationSpeciesStructure
(parent, labels, list)¶ Bases:
sage.combinat.species.structure.GenericSpeciesStructure
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automorphism_group
()¶ Returns the group of permutations whose action on this structure leave it fixed.
EXAMPLES:
sage: set_random_seed(0) sage: p = PermutationGroupElement((2,3,4)) sage: P = species.PermutationSpecies() sage: a = P.structures(["a", "b", "c", "d"])[2]; a ['a', 'c', 'b', 'd'] sage: a.automorphism_group() Permutation Group with generators [(2,3), (1,4)]
sage: [a.transport(perm) for perm in a.automorphism_group()] [['a', 'c', 'b', 'd'], ['a', 'c', 'b', 'd'], ['a', 'c', 'b', 'd'], ['a', 'c', 'b', 'd']]
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canonical_label
()¶ EXAMPLES:
sage: P = species.PermutationSpecies() sage: S = P.structures(["a", "b", "c"]) sage: [s.canonical_label() for s in S] [['a', 'b', 'c'], ['b', 'a', 'c'], ['b', 'a', 'c'], ['b', 'c', 'a'], ['b', 'c', 'a'], ['b', 'a', 'c']]
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permutation_group_element
()¶ Returns self as a permutation group element.
EXAMPLES:
sage: p = PermutationGroupElement((2,3,4)) sage: P = species.PermutationSpecies() sage: a = P.structures(["a", "b", "c", "d"])[2]; a ['a', 'c', 'b', 'd'] sage: a.permutation_group_element() (2,3)
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transport
(perm)¶ Returns the transport of this structure along the permutation perm.
EXAMPLES:
sage: p = PermutationGroupElement((2,3,4)) sage: P = species.PermutationSpecies() sage: a = P.structures(["a", "b", "c", "d"])[2]; a ['a', 'c', 'b', 'd'] sage: a.transport(p) ['a', 'd', 'c', 'b']
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sage.combinat.species.permutation_species.
PermutationSpecies_class
¶ alias of
sage.combinat.species.permutation_species.PermutationSpecies