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Mathematics Mathematica Discrete Mathematics Group Theory

How can I get Permutations of each Integer Partition?

Logan Bell

Posted 10 years ago

Hello! Before we begin, let me mention that I am rubbish at coding. Ok! Time to explain my question a bit more. What I'm trying to do is get each permutation of each integer partition. You see, if I do IntegerPartitions[7} I get a single permutation of each list. For example, I might get {2,2,1,1,1} as an answer, but I won't get {1,2,1,2,1} and {2,2,1,1,1} as answers. So far, I've been manually taking each list and putting it into code, but this takes a while if I'm doing it for each one. Permutations[{2,2,1,1,1}] Depending on how large the number is for the IntegerPartitions step, there could be more than a hundred answers, so to manually copy over each list to the Permutations code would take a while. My question is, how would I get each permutation of each partition without having to manually copy over each partition into the permutation code? Thanks for any help! :)

POSTED BY: Logan Bell

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Daniel Lichtblau

Daniel Lichtblau, Wolfram Research

Posted 10 years ago

If I understand correctly the question, then you just want to use `Map`. Map[Permutations, IntegerPartitions[7]] (* Out[183]= {{{7}}, {{6, 1}, {1, 6}}, {{5, 2}, {2, 5}}, {{5, 1, 1}, {1, 5, 1}, {1, 1, 5}}, {{4, 3}, {3, 4}}, {{4, 2, 1}, {4, 1, 2}, {2, 4, 1}, {2, 1, 4}, {1, 4, 2}, {1, 2, 4}}, {{4, 1, 1, 1}, {1, 4, 1, 1}, {1, 1, 4, 1}, {1, 1, 1, 4}}, {{3, 3, 1}, {3, 1, 3}, {1, 3, 3}}, {{3, 2, 2}, {2, 3, 2}, {2, 2, 3}}, {{3, 2, 1, 1}, {3, 1, 2, 1}, {3, 1, 1, 2}, {2, 3, 1, 1}, {2, 1, 3, 1}, {2, 1, 1, 3}, {1, 3, 2, 1}, {1, 3, 1, 2}, {1, 2, 3, 1}, {1, 2, 1, 3}, {1, 1, 3, 2}, {1, 1, 2, 3}}, {{3, 1, 1, 1, 1}, {1, 3, 1, 1, 1}, {1, 1, 3, 1, 1}, {1, 1, 1, 3, 1}, {1, 1, 1, 1, 3}}, {{2, 2, 2, 1}, {2, 2, 1, 2}, {2, 1, 2, 2}, {1, 2, 2, 2}}, {{2, 2, 1, 1, 1}, {2, 1, 2, 1, 1}, {2, 1, 1, 2, 1}, {2, 1, 1, 1, 2}, {1, 2, 2, 1, 1}, {1, 2, 1, 2, 1}, {1, 2, 1, 1, 2}, {1, 1, 2, 2, 1}, {1, 1, 2, 1, 2}, {1, 1, 1, 2, 2}}, {{2, 1, 1, 1, 1, 1}, {1, 2, 1, 1, 1, 1}, {1, 1, 2, 1, 1, 1}, {1, 1, 1, 2, 1, 1}, {1, 1, 1, 1, 2, 1}, {1, 1, 1, 1, 1, 2}}, {{1, 1, 1, 1, 1, 1, 1}}} *)

If I understand correctly the question, then you just want to use Map.

Map[Permutations, IntegerPartitions[7]]

(* Out[183]= {{{7}}, {{6, 1}, {1, 6}}, {{5, 2}, {2, 5}}, {{5, 1, 1}, {1, 
   5, 1}, {1, 1, 5}}, {{4, 3}, {3, 4}}, {{4, 2, 1}, {4, 1, 2}, {2, 4, 
   1}, {2, 1, 4}, {1, 4, 2}, {1, 2, 4}}, {{4, 1, 1, 1}, {1, 4, 1, 
   1}, {1, 1, 4, 1}, {1, 1, 1, 4}}, {{3, 3, 1}, {3, 1, 3}, {1, 3, 
   3}}, {{3, 2, 2}, {2, 3, 2}, {2, 2, 3}}, {{3, 2, 1, 1}, {3, 1, 2, 
   1}, {3, 1, 1, 2}, {2, 3, 1, 1}, {2, 1, 3, 1}, {2, 1, 1, 3}, {1, 3, 
   2, 1}, {1, 3, 1, 2}, {1, 2, 3, 1}, {1, 2, 1, 3}, {1, 1, 3, 2}, {1, 
   1, 2, 3}}, {{3, 1, 1, 1, 1}, {1, 3, 1, 1, 1}, {1, 1, 3, 1, 1}, {1, 
   1, 1, 3, 1}, {1, 1, 1, 1, 3}}, {{2, 2, 2, 1}, {2, 2, 1, 2}, {2, 1, 
   2, 2}, {1, 2, 2, 2}}, {{2, 2, 1, 1, 1}, {2, 1, 2, 1, 1}, {2, 1, 1, 
   2, 1}, {2, 1, 1, 1, 2}, {1, 2, 2, 1, 1}, {1, 2, 1, 2, 1}, {1, 2, 1,
    1, 2}, {1, 1, 2, 2, 1}, {1, 1, 2, 1, 2}, {1, 1, 1, 2, 2}}, {{2, 1,
    1, 1, 1, 1}, {1, 2, 1, 1, 1, 1}, {1, 1, 2, 1, 1, 1}, {1, 1, 1, 2, 
   1, 1}, {1, 1, 1, 1, 2, 1}, {1, 1, 1, 1, 1, 2}}, {{1, 1, 1, 1, 1, 1,
    1}}} *)

POSTED BY: Daniel Lichtblau

Logan Bell

Posted 10 years ago

Cool! Thanks! :)

POSTED BY: Logan Bell

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