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How to get a list of the combinations such that the elements are equal to some $n$

asked 2018-09-03 20:45:31 -0500

MarioM gravatar image

updated 2018-09-03 20:47:37 -0500

I want a generalization of this kind

[(r1, ..., rk) for r1 in range(n+1) ... for rk in range(n+1) if r1 + ... + rk = n]

For a general number of $r$'s and any $n$

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answered 2018-09-04 00:47:34 -0500

tmonteil gravatar image

You can use IntegerListsLex (see the documentation for all options):

sage: C = IntegerListsLex(6, length=4)

sage: C.list()
[[6, 0, 0, 0],
 [5, 1, 0, 0],
 [5, 0, 1, 0],
 [5, 0, 0, 1],
 [4, 2, 0, 0],
 [4, 1, 1, 0],
 [4, 1, 0, 1],
 [4, 0, 2, 0],
 [4, 0, 1, 1],
 [4, 0, 0, 2],
 [3, 3, 0, 0],
 [3, 2, 1, 0],
 [3, 2, 0, 1],
 [3, 1, 2, 0],
 [3, 1, 1, 1],
 [3, 1, 0, 2],
 [3, 0, 3, 0],
 [3, 0, 2, 1],
 [3, 0, 1, 2],
 [3, 0, 0, 3],
 [2, 4, 0, 0],
 [2, 3, 1, 0],
 [2, 3, 0, 1],
 [2, 2, 2, 0],
 [2, 2, 1, 1],
 [2, 2, 0, 2],
 [2, 1, 3, 0],
 [2, 1, 2, 1],
 [2, 1, 1, 2],
 [2, 1, 0, 3],
 [2, 0, 4, 0],
 [2, 0, 3, 1],
 [2, 0, 2, 2],
 [2, 0, 1, 3],
 [2, 0, 0, 4],
 [1, 5, 0, 0],
 [1, 4, 1, 0],
 [1, 4, 0, 1],
 [1, 3, 2, 0],
 [1, 3, 1, 1],
 [1, 3, 0, 2],
 [1, 2, 3, 0],
 [1, 2, 2, 1],
 [1, 2, 1, 2],
 [1, 2, 0, 3],
 [1, 1, 4, 0],
 [1, 1, 3, 1],
 [1, 1, 2, 2],
 [1, 1, 1, 3],
 [1, 1, 0, 4],
 [1, 0, 5, 0],
 [1, 0, 4, 1],
 [1, 0, 3, 2],
 [1, 0, 2, 3],
 [1, 0, 1, 4],
 [1, 0, 0, 5],
 [0, 6, 0, 0],
 [0, 5, 1, 0],
 [0, 5, 0, 1],
 [0, 4, 2, 0],
 [0, 4, 1, 1],
 [0, 4, 0, 2],
 [0, 3, 3, 0],
 [0, 3, 2, 1],
 [0, 3, 1, 2],
 [0, 3, 0, 3],
 [0, 2, 4, 0],
 [0, 2, 3, 1],
 [0, 2, 2, 2],
 [0, 2, 1, 3],
 [0, 2, 0, 4],
 [0, 1, 5, 0],
 [0, 1, 4, 1],
 [0, 1, 3, 2],
 [0, 1, 2, 3],
 [0, 1, 1, 4],
 [0, 1, 0, 5],
 [0, 0, 6, 0],
 [0, 0, 5, 1],
 [0, 0, 4, 2],
 [0, 0, 3, 3],
 [0, 0, 2, 4],
 [0, 0, 1, 5],
 [0, 0, 0, 6]]
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Thank you i will see the documentation

MarioM gravatar imageMarioM ( 2018-09-04 09:36:37 -0500 )edit

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Asked: 2018-09-03 20:45:31 -0500

Seen: 34 times

Last updated: Sep 04