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)
__contains__(x)

EXAMPLES:

sage: c = Combinations(range(4))
sage: all( i in c for i in c )
True
sage: [3,4] in c
False
sage: [0,0] in c
False
__init__(mset)

TESTS:

sage: C = Combinations(range(4))
sage: C == loads(dumps(C))
True
__iter__()

TESTS:

sage: Combinations(['a','a','b']).list() #indirect doctest
[[], ['a'], ['b'], ['a', 'a'], ['a', 'b'], ['a', 'a', 'b']]
__repr__()

TESTS:

sage: repr(Combinations(range(4)))
'Combinations of [0, 1, 2, 3]'
cardinality()

TESTS:

sage: Combinations([1,2,3]).cardinality()
8
sage: Combinations(['a','a','b']).cardinality()
6
class sage.combinat.combination.Combinations_msetk(mset, k)
__contains__(x)

EXAMPLES:

sage: c = Combinations(range(4),2)
sage: all( i in c for i in c )
True
sage: [0,1] in c
True
sage: [0,1,2] in c
False
sage: [3,4] in c
False
sage: [0,0] in c
False
__init__(mset, k)

TESTS:

sage: C = Combinations([1,2,3],2)
sage: C == loads(dumps(C))
True
__iter__()

EXAMPLES:

sage: Combinations(['a','a','b'],2).list() # indirect doctest
[['a', 'a'], ['a', 'b']]
__repr__()

TESTS:

sage: repr(Combinations([1,2,2,3],2))
'Combinations of [1, 2, 2, 3] of length 2'
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)
__iter__()

EXAMPLES:

sage: Combinations([1,2,3]).list() #indirect doctest
[[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]
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)
__iter__()

Posted by Raymond Hettinger, 2006/03/23, to the Python Cookbook: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/474124

EXAMPLES:

sage: Combinations([1,2,3,4,5],3).list() # indirect doctest
[[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]]
_iterator(items, len_items, n)

An iterator for all the n-combinations of items.

EXAMPLES:

sage: it = Combinations([1,2,3,4],3)._iterator([1,2,3,4],4,3)
sage: list(it)
[[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]]
_iterator_zero()

An iterator which just returns the empty list.

EXAMPLES:

sage: it = Combinations([1,2,3,4,5],3)._iterator_zero()
sage: list(it)
[[]]
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

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