Find all permutations with a condition (part 2)

Question

This question (21008) asks to find all permutations of {a, b, c} subject to a + b + c = n. The answer was provided by Dr. belisarius using IntegerPartitions.

How can we generalize that answer to find all permutations of {a, b, c} subject to 2 a + b + c = const, or more generally find all partitions subject to {a, b, c, d, e, ...} subject to 2 a + b + c + d + e + ... = n?

score 3 · Accepted Answer · answered Jun 11 '17 at 19:56

3

Are you looking for FrobeniusSolve? e.g. for $2 a + b + c = 5$

FrobeniusSolve[{2, 1, 1}, 5]

{{0, 0, 5}, {0, 1, 4}, {0, 2, 3}, {0, 3, 2}, {0, 4, 1}, {0, 5, 0},
 {1, 0, 3},  {1, 1, 2}, {1, 2, 1}, {1, 3, 0}, {2, 0, 1}, {2, 1, 0}}

answered Jun 11 '17 at 19:56

Mr.Wizard

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facepalm! * If the answer is that simple, then the best thing to do is to accept this answer, and close this question because "it can easily be found in the documentation".

QuantumDot

Jun 11 '17 at 20:16

@QuantumDot It happens to all of us. :^) – Mr.Wizard Jun 11 '17 at 20:20

score 1 · Answer 2 · answered Jun 11 '17 at 19:45

How about:

g[sz_, n_] := Partition[Flatten[Map[Thread[{
    #/2, f[n - #, sz - 1]}] &, Range[0, n, 2]]], sz]
g[3, 5]

{{0, 5, 0}, {0, 0, 5}, {0, 4, 1}, {0, 1, 4}, {0, 3, 2}, {0, 2, 3}, {1, 3, 0}, {1, 0, 3}, {1, 2, 1}, {1, 1, 2}, {2, 1, 0}, {2, 0, 1}}

where f is defined in the question you mentioned:

f[sum_, quant_] := Flatten[Permutations /@
                    IntegerPartitions[sum, {quant}, Range[0, sum]], 1]

Find all permutations with a condition (part 2)

2 Answers2