# Tuples¶

sage.combinat.tuple.Tuples(S, k)

Returns the combinatorial class of ordered tuples of S of length k.

An ordered tuple of length k of set is an ordered selection with repetition and is represented by a list of length k containing elements of set.

EXAMPLES:

sage: S = [1,2]
sage: Tuples(S,3).list()
[[1, 1, 1], [2, 1, 1], [1, 2, 1], [2, 2, 1], [1, 1, 2], [2, 1, 2], [1, 2, 2], [2, 2, 2]]
sage: mset = ["s","t","e","i","n"]
sage: Tuples(mset,2).list()
[['s', 's'], ['t', 's'], ['e', 's'], ['i', 's'], ['n', 's'], ['s', 't'], ['t', 't'],
['e', 't'], ['i', 't'], ['n', 't'], ['s', 'e'], ['t', 'e'], ['e', 'e'], ['i', 'e'],
['n', 'e'], ['s', 'i'], ['t', 'i'], ['e', 'i'], ['i', 'i'], ['n', 'i'], ['s', 'n'],
['t', 'n'], ['e', 'n'], ['i', 'n'], ['n', 'n']]

sage: K.<a> = GF(4, 'a')
sage: mset = [x for x in K if x!=0]
sage: Tuples(mset,2).list()
[[a, a], [a + 1, a], [1, a], [a, a + 1], [a + 1, a + 1], [1, a + 1], [a, 1], [a + 1, 1], [1, 1]]

class sage.combinat.tuple.Tuples_sk(S, k)

TESTS:

sage: T = Tuples([1,2,3],2)
True

cardinality()

EXAMPLES:

sage: S = [1,2,3,4,5]
sage: Tuples(S,2).cardinality()
25
sage: S = [1,1,2,3,4,5]
sage: Tuples(S,2).cardinality()
25

sage.combinat.tuple.UnorderedTuples(S, k)

Returns the combinatorial class of unordered tuples of S of length k.

An unordered tuple of length k of set is a unordered selection with repetitions of set and is represented by a sorted list of length k containing elements from set.

EXAMPLES:

sage: S = [1,2]
sage: UnorderedTuples(S,3).list()
[[1, 1, 1], [1, 1, 2], [1, 2, 2], [2, 2, 2]]
sage: UnorderedTuples(["a","b","c"],2).list()
[['a', 'a'], ['a', 'b'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['c', 'c']]

class sage.combinat.tuple.UnorderedTuples_sk(S, k)

TESTS:

sage: T = Tuples([1,2,3],2)
True

cardinality()

EXAMPLES:

sage: S = [1,2,3,4,5]
sage: UnorderedTuples(S,2).cardinality()
15

list()

EXAMPLES:

sage: S = [1,2]
sage: UnorderedTuples(S,3).list()
[[1, 1, 1], [1, 1, 2], [1, 2, 2], [2, 2, 2]]
sage: UnorderedTuples(["a","b","c"],2).list()
[['a', 'a'], ['a', 'b'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['c', 'c']]


Tools

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Introduction to combinatorics in Sage