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Identifier

St001735: Permutations ⟶ ℤ

Values

[1] => 1

[1,2] => 1

[2,1] => 1

[1,2,3] => 1

[1,3,2] => 2

[2,1,3] => 2

[2,3,1] => 1

[3,1,2] => 1

[3,2,1] => 1

[1,2,3,4] => 1

[1,2,4,3] => 2

[1,3,2,4] => 2

[1,3,4,2] => 2

[1,4,2,3] => 2

[1,4,3,2] => 4

[2,1,3,4] => 2

[2,1,4,3] => 4

[2,3,1,4] => 2

[2,3,4,1] => 1

[2,4,1,3] => 2

[2,4,3,1] => 2

[3,1,2,4] => 2

[3,1,4,2] => 4

[3,2,1,4] => 4

[3,2,4,1] => 2

[3,4,1,2] => 1

[3,4,2,1] => 1

[4,1,2,3] => 1

[4,1,3,2] => 2

[4,2,1,3] => 2

[4,2,3,1] => 1

[4,3,1,2] => 1

[4,3,2,1] => 1

[1,2,3,4,5] => 1

[1,2,3,5,4] => 2

[1,2,4,3,5] => 2

[1,2,4,5,3] => 2

[1,2,5,3,4] => 2

[1,2,5,4,3] => 4

[1,3,2,4,5] => 2

[1,3,2,5,4] => 4

[1,3,4,2,5] => 2

[1,3,4,5,2] => 2

[1,3,5,2,4] => 2

[1,3,5,4,2] => 4

[1,4,2,3,5] => 2

[1,4,2,5,3] => 6

[1,4,3,2,5] => 6

[1,4,3,5,2] => 4

[1,4,5,2,3] => 2

[1,4,5,3,2] => 4

[1,5,2,3,4] => 2

[1,5,2,4,3] => 6

[1,5,3,2,4] => 6

[1,5,3,4,2] => 4

[1,5,4,2,3] => 4

[1,5,4,3,2] => 8

[2,1,3,4,5] => 2

[2,1,3,5,4] => 4

[2,1,4,3,5] => 4

[2,1,4,5,3] => 4

[2,1,5,3,4] => 4

[2,1,5,4,3] => 8

[2,3,1,4,5] => 2

[2,3,1,5,4] => 4

[2,3,4,1,5] => 2

[2,3,4,5,1] => 1

[2,3,5,1,4] => 2

[2,3,5,4,1] => 2

[2,4,1,3,5] => 2

[2,4,1,5,3] => 6

[2,4,3,1,5] => 6

[2,4,3,5,1] => 2

[2,4,5,1,3] => 2

[2,4,5,3,1] => 2

[2,5,1,3,4] => 2

[2,5,1,4,3] => 6

[2,5,3,1,4] => 6

[2,5,3,4,1] => 2

[2,5,4,1,3] => 4

[2,5,4,3,1] => 4

[3,1,2,4,5] => 2

[3,1,2,5,4] => 4

[3,1,4,2,5] => 6

[3,1,4,5,2] => 4

[3,1,5,2,4] => 6

[3,1,5,4,2] => 8

[3,2,1,4,5] => 4

[3,2,1,5,4] => 8

[3,2,4,1,5] => 6

[3,2,4,5,1] => 2

[3,2,5,1,4] => 6

[3,2,5,4,1] => 4

[3,4,1,2,5] => 2

[3,4,1,5,2] => 4

[3,4,2,1,5] => 4

[3,4,2,5,1] => 2

[3,4,5,1,2] => 1

[3,4,5,2,1] => 1

[3,5,1,2,4] => 2

[3,5,1,4,2] => 4

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Description

The number of permutations with the same set of runs.
For example, the set of runs of $4132$ is $\{(13), (2), (4)\}$. The only other permutation with this set of runs is $4213$, so the statistic equals $2$ for these two permutations.

Code

def statistic(pi):
    runs = sorted(tuple(r) for r in pi.runs())
    c = 0
    for permuted_runs in Permutations(runs):
        sigma = Permutation([e for r in permuted_runs for e in r])
        if sorted(tuple(r) for r in sigma.runs()) == runs:
            c += 1
    return c

Created

Aug 23, 2021 at 12:07 by Martin Rubey

Updated

Sep 13, 2021 at 13:43 by Martin Rubey