Combinations

sage.combinat.combination.Combinations(mset, k=None)

Returns the combinatorial class of combinations of mset. If k is specified, then it returns the combinatorial class of combinations of mset of size k.

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]]

class sage.combinat.combination.Combinations_mset(mset)

Bases: sage.combinat.combinat.CombinatorialClass

cardinality()

TESTS:

sage: Combinations([1,2,3]).cardinality()
8
sage: Combinations(['a','a','b']).cardinality()
6

class sage.combinat.combination.Combinations_msetk(mset, k)

Bases: sage.combinat.combinat.CombinatorialClass

cardinality()

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

class sage.combinat.combination.Combinations_set(mset)

Bases: sage.combinat.combination.Combinations_mset

rank(x)

EXAMPLES:

sage: c = Combinations([1,2,3])
sage: range(c.cardinality()) == map(c.rank, c)
True

unrank(r)

EXAMPLES:

sage: c = Combinations([1,2,3])
sage: c.list() == map(c.unrank, range(c.cardinality()))
True

class sage.combinat.combination.Combinations_setk(mset, k)

Bases: sage.combinat.combination.Combinations_msetk

list()

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]]

rank(x)

EXAMPLES:

sage: c = Combinations([1,2,3], 2)
sage: range(c.cardinality()) == map(c.rank, c.list())
True

unrank(r)

EXAMPLES:

sage: c = Combinations([1,2,3], 2)
sage: c.list() == map(c.unrank, range(c.cardinality()))
True