Characteristic Species

class sage.combinat.species.characteristic_species.CharacteristicSpeciesStructure(parent, labels, list)

Bases: sage.combinat.species.structure.GenericSpeciesStructure

automorphism_group()

Returns the group of permutations whose action on this structure leave it fixed. For the characteristic species, there is only one structure, so every permutation is in its automorphism group.

EXAMPLES:

sage: F = species.CharacteristicSpecies(3)
sage: a = F.structures(["a", "b", "c"]).random_element(); a
{'a', 'b', 'c'}
sage: a.automorphism_group()
Symmetric group of order 3! as a permutation group

canonical_label()

EXAMPLES:

sage: F = species.CharacteristicSpecies(3)
sage: a = F.structures(["a", "b", "c"]).random_element(); a
{'a', 'b', 'c'}
sage: a.canonical_label()
{'a', 'b', 'c'}

transport(perm)

Returns the transport of this structure along the permutation perm.

EXAMPLES:

sage: F = species.CharacteristicSpecies(3)
sage: a = F.structures(["a", "b", "c"]).random_element(); a
{'a', 'b', 'c'}
sage: p = PermutationGroupElement((1,2))
sage: a.transport(p)
{'a', 'b', 'c'}

class sage.combinat.species.characteristic_species.CharacteristicSpecies_class(n, min=None, max=None, weight=None)

Bases: sage.combinat.species.species.GenericCombinatorialSpecies

class sage.combinat.species.characteristic_species.EmptySetSpecies_class(min=None, max=None, weight=None)

Bases: sage.combinat.species.characteristic_species.CharacteristicSpecies_class

class sage.combinat.species.characteristic_species.SingletonSpecies_class(min=None, max=None, weight=None)

Bases: sage.combinat.species.characteristic_species.CharacteristicSpecies_class