# Deprecated combinations¶

AUTHORS:

• Mike Hansen (2007): initial implementation
• Vincent Delecroix (2014): deprecation
sage.combinat.choose_nk.ChooseNK(n, k)

All possible choices of k elements out of range(n) without repetitions.

The elements of the output are tuples of Python int (and not Sage Integer).

This was deprecated in trac ticket #10534 for Combinations() (or itertools.combinations for doing iteration).

EXAMPLES:

sage: from sage.combinat.choose_nk import ChooseNK
sage: c = ChooseNK(4,2)
doctest:...: DeprecationWarning: ChooseNk is deprecated and will be
removed. Use Combinations instead (or combinations from the itertools
module for iteration)
See http://trac.sagemath.org/10534 for details.
sage: c.first()
[0, 1]
sage: c.list()
[[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]]

sage.combinat.choose_nk.from_rank(r, n, k)

Returns the combination of rank r in the subsets of range(n) of size k when listed in lexicographic order.

The algorithm used is based on combinadics and James McCaffrey’s MSDN article. See: http://en.wikipedia.org/wiki/Combinadic

EXAMPLES:

sage: import sage.combinat.choose_nk as choose_nk
sage: choose_nk.from_rank(0,3,0)
()
sage: choose_nk.from_rank(0,3,1)
(0,)
sage: choose_nk.from_rank(1,3,1)
(1,)
sage: choose_nk.from_rank(2,3,1)
(2,)
sage: choose_nk.from_rank(0,3,2)
(0, 1)
sage: choose_nk.from_rank(1,3,2)
(0, 2)
sage: choose_nk.from_rank(2,3,2)
(1, 2)
sage: choose_nk.from_rank(0,3,3)
(0, 1, 2)

sage.combinat.choose_nk.rank(comb, n, check=True)

Return the rank of comb in the subsets of range(n) of size k where k is the length of comb.

The algorithm used is based on combinadics and James McCaffrey’s MSDN article. See: Wikipedia article Combinadic.

EXAMPLES:

sage: import sage.combinat.choose_nk as choose_nk
sage: choose_nk.rank((), 3)
0
sage: choose_nk.rank((0,), 3)
0
sage: choose_nk.rank((1,), 3)
1
sage: choose_nk.rank((2,), 3)
2
sage: choose_nk.rank((0,1), 3)
0
sage: choose_nk.rank((0,2), 3)
1
sage: choose_nk.rank((1,2), 3)
2
sage: choose_nk.rank((0,1,2), 3)
0

sage: choose_nk.rank((0,1,2,3), 3)
Traceback (most recent call last):
...
ValueError: len(comb) must be <= n
sage: choose_nk.rank((0,0), 2)
Traceback (most recent call last):
...
ValueError: comb must be a subword of (0,1,...,n)

sage: choose_nk.rank([1,2], 3)
2
sage: choose_nk.rank([0,1,2], 3)
0


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