Signed Compositions

sage.combinat.composition_signed.SignedCompositions(n)

Returns the combinatorial class of signed compositions of n.

EXAMPLES:

sage: SC3 = SignedCompositions(3); SC3
Signed compositions of 3
sage: SC3.cardinality()
18
sage: len(SC3.list())
18
sage: SC3.first()
[1, 1, 1]
sage: SC3.last()
[-3]
sage: SC3.random_element()
[1, -1, 1]
sage: SC3.list()
[[1, 1, 1],
 [1, 1, -1],
 [1, -1, 1],
 [1, -1, -1],
 [-1, 1, 1],
 [-1, 1, -1],
 [-1, -1, 1],
 [-1, -1, -1],
 [1, 2],
 [1, -2],
 [-1, 2],
 [-1, -2],
 [2, 1],
 [2, -1],
 [-2, 1],
 [-2, -1],
 [3],
 [-3]]

class sage.combinat.composition_signed.SignedCompositions_n(n)

Bases: sage.combinat.combinat.CombinatorialClass

cardinality()

TESTS:

sage: SC4 = SignedCompositions(4)
sage: SC4.cardinality() == len(SC4.list())
True
sage: SignedCompositions(3).cardinality()
18