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# Set Species

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

  Bases: `sage.combinat.species.species.GenericCombinatorialSpecies`, `sage.structure.unique_representation.UniqueRepresentation`

  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
      sage: S == loads(dumps(S))
      True

class `sage.combinat.species.set_species.``SetSpeciesStructure`(parent, labels, list)

  Bases: `sage.combinat.species.structure.GenericSpeciesStructure`

  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
      sage: a == loads(dumps(a))
      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`

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