AUTHORS:
Bases: sage.combinat.combination.Combinations_setk
TESTS:
sage: C = Combinations([1,2,3],2)
sage: C == loads(dumps(C))
True
Return the combinatorial class of combinations of the multiset mset. If k is specified, then it returns the combinatorial class of combinations of mset of size k.
A combination of a multiset is an unordered selection of
objects of
, where every object can appear at most as many
times as it appears in
.
The combinatorial classes correctly handle the cases where mset has duplicate elements.
EXAMPLES:
sage: C = Combinations(range(4)); C
Combinations of [0, 1, 2, 3]
sage: C.list()
[[],
[0],
[1],
[2],
[3],
[0, 1],
[0, 2],
[0, 3],
[1, 2],
[1, 3],
[2, 3],
[0, 1, 2],
[0, 1, 3],
[0, 2, 3],
[1, 2, 3],
[0, 1, 2, 3]]
sage: C.cardinality()
16
sage: C2 = Combinations(range(4),2); C2
Combinations of [0, 1, 2, 3] of length 2
sage: C2.list()
[[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]]
sage: C2.cardinality()
6
sage: Combinations([1,2,2,3]).list()
[[],
[1],
[2],
[3],
[1, 2],
[1, 3],
[2, 2],
[2, 3],
[1, 2, 2],
[1, 2, 3],
[2, 2, 3],
[1, 2, 2, 3]]
sage: Combinations([1,2,3], 2).list()
[[1, 2], [1, 3], [2, 3]]
sage: mset = [1,1,2,3,4,4,5]
sage: Combinations(mset,2).list()
[[1, 1],
[1, 2],
[1, 3],
[1, 4],
[1, 5],
[2, 3],
[2, 4],
[2, 5],
[3, 4],
[3, 5],
[4, 4],
[4, 5]]
sage: mset = ["d","a","v","i","d"]
sage: Combinations(mset,3).list()
[['d', 'd', 'a'],
['d', 'd', 'v'],
['d', 'd', 'i'],
['d', 'a', 'v'],
['d', 'a', 'i'],
['d', 'v', 'i'],
['a', 'v', 'i']]
sage: X = Combinations([1,2,3,4,5],3)
sage: [x for x in X]
[[1, 2, 3],
[1, 2, 4],
[1, 2, 5],
[1, 3, 4],
[1, 3, 5],
[1, 4, 5],
[2, 3, 4],
[2, 3, 5],
[2, 4, 5],
[3, 4, 5]]
It is possible to take combinations of Sage objects:
sage: Combinations([vector([1,1]), vector([2,2]), vector([3,3])], 2).list()
[[(1, 1), (2, 2)], [(1, 1), (3, 3)], [(2, 2), (3, 3)]]
TESTS:
We check that the code works even for non mutable objects:
sage: l = [vector((0,0)), vector((0,1))]
sage: Combinations(l).list()
[[], [(0, 0)], [(0, 1)], [(0, 0), (0, 1)]]
Bases: sage.combinat.combinat.CombinatorialClass
TESTS:
sage: C = Combinations(range(4))
sage: C == loads(dumps(C))
True
TESTS:
sage: Combinations([1,2,3]).cardinality()
8
sage: Combinations(['a','a','b']).cardinality()
6
Bases: sage.combinat.combinat.CombinatorialClass
TESTS:
sage: C = Combinations([1,2,3],2)
sage: C == loads(dumps(C))
True
Returns the size of combinations(mset,k). IMPLEMENTATION: Wraps GAP’s NrCombinations.
EXAMPLES:
sage: mset = [1,1,2,3,4,4,5]
sage: Combinations(mset,2).cardinality()
12
Bases: sage.combinat.combination.Combinations_mset
TESTS:
sage: C = Combinations(range(4))
sage: C == loads(dumps(C))
True
EXAMPLES:
sage: c = Combinations([1,2,3])
sage: range(c.cardinality()) == map(c.rank, c)
True
EXAMPLES:
sage: c = Combinations([1,2,3])
sage: c.list() == map(c.unrank, range(c.cardinality()))
True
Bases: sage.combinat.combination.Combinations_msetk
TESTS:
sage: C = Combinations([1,2,3],2)
sage: C == loads(dumps(C))
True
EXAMPLES:
sage: Combinations([1,2,3,4,5],3).list()
[[1, 2, 3],
[1, 2, 4],
[1, 2, 5],
[1, 3, 4],
[1, 3, 5],
[1, 4, 5],
[2, 3, 4],
[2, 3, 5],
[2, 4, 5],
[3, 4, 5]]
EXAMPLES:
sage: c = Combinations([1,2,3], 2)
sage: range(c.cardinality()) == map(c.rank, c.list())
True
EXAMPLES:
sage: c = Combinations([1,2,3], 2)
sage: c.list() == map(c.unrank, range(c.cardinality()))
True