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)
__contains__(x)

TESTS:

sage: [] in SignedCompositions(0)
True
sage: [0] in SignedCompositions(0)
False
sage: [2,1,3] in SignedCompositions(6)
True
sage: [-2, 1, -3] in SignedCompositions(6)
True
__init__(n)

TESTS:

sage: SC3 = SignedCompositions(3)
sage: SC3 == loads(dumps(SC3))
True
__iter__()

TESTS:

sage: SignedCompositions(0).list()   #indirect doctest
[[]]
sage: SignedCompositions(1).list()   #indirect doctest
[[1], [-1]]
sage: SignedCompositions(2).list()   #indirect doctest
[[1, 1], [1, -1], [-1, 1], [-1, -1], [2], [-2]]
__repr__()

TESTS:

sage: repr(SignedCompositions(3))
'Signed compositions of 3'
cardinality()

TESTS:

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

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