Set Species¶

class sage.combinat.species.set_species.SetSpecies(min=None, max=None, weight=None)

Returns the species of sets.

EXAMPLES:

sage: E = species.SetSpecies()
sage: E.structures([1,2,3]).list()
[{1, 2, 3}]
sage: E.isotype_generating_series().coefficients(4)
[1, 1, 1, 1]

sage: S = species.SetSpecies()
sage: c = S.generating_series().coefficients(3)
sage: S._check()
True
True
class sage.combinat.species.set_species.SetSpeciesStructure(parent, labels, list)

EXAMPLES:

sage: from sage.combinat.species.structure import GenericSpeciesStructure
sage: a = GenericSpeciesStructure(None, [2,3,4], [1,2,3])
sage: a
[2, 3, 4]
sage: a.parent() is None
True
True
automorphism_group()

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

EXAMPLES:

sage: F = species.SetSpecies()
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: S = species.SetSpecies()
sage: a = S.structures(["a","b","c"]).random_element(); a
{'a', 'b', 'c'}
sage: a.canonical_label()
{'a', 'b', 'c'}
transport(perm)

Returns the transport of this set along the permutation perm.

EXAMPLES:

sage: F = species.SetSpecies()
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'}
sage.combinat.species.set_species.SetSpecies_class

alias of SetSpecies

Previous topic

Linear-order Species

Subset Species