Cycle Species¶
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class
sage.combinat.species.cycle_species.
CycleSpecies
(min=None, max=None, weight=None)¶ Bases:
sage.combinat.species.species.GenericCombinatorialSpecies
,sage.structure.unique_representation.UniqueRepresentation
Returns the species of cycles.
EXAMPLES:
sage: C = species.CycleSpecies(); C Cyclic permutation species sage: C.structures([1,2,3,4]).list() [(1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 2, 4), (1, 3, 4, 2), (1, 4, 2, 3), (1, 4, 3, 2)]
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class
sage.combinat.species.cycle_species.
CycleSpeciesStructure
(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: P = species.CycleSpecies() sage: a = P.structures([1, 2, 3, 4])[0]; a (1, 2, 3, 4) sage: a.automorphism_group() Permutation Group with generators [(1,2,3,4)]
sage: [a.transport(perm) for perm in a.automorphism_group()] [(1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4)]
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canonical_label
()¶ EXAMPLES:
sage: P = species.CycleSpecies() sage: P.structures(["a","b","c"]).random_element().canonical_label() ('a', 'b', 'c')
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permutation_group_element
()¶ Returns this cycle as a permutation group element.
EXAMPLES:
sage: F = species.CycleSpecies() sage: a = F.structures(["a", "b", "c"])[0]; a ('a', 'b', 'c') sage: a.permutation_group_element() (1,2,3)
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transport
(perm)¶ Returns the transport of this structure along the permutation perm.
EXAMPLES:
sage: F = species.CycleSpecies() sage: a = F.structures(["a", "b", "c"])[0]; a ('a', 'b', 'c') sage: p = PermutationGroupElement((1,2)) sage: a.transport(p) ('a', 'c', 'b')
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sage.combinat.species.cycle_species.
CycleSpecies_class
¶