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Identifier
Values
[1] => 1
[2] => 1
[1,1] => 1
[3] => 0
[2,1] => 1
[1,1,1] => 3
[4] => 1
[3,1] => 0
[2,2] => 1
[2,1,1] => 1
[1,1,1,1] => 9
[5] => 1
[4,1] => 1
[3,2] => 0
[3,1,1] => 0
[2,2,1] => 1
[2,1,1,1] => 3
[1,1,1,1,1] => 21
[6] => 0
[5,1] => 1
[4,2] => 1
[4,1,1] => 1
[3,3] => 0
[3,2,1] => 0
[3,1,1,1] => 0
[2,2,2] => 9
[2,2,1,1] => 1
[2,1,1,1,1] => 9
[1,1,1,1,1,1] => 81
[7] => 1
[6,1] => 0
[5,2] => 1
[5,1,1] => 1
[4,3] => 0
[4,2,1] => 1
[4,1,1,1] => 3
[3,3,1] => 0
[3,2,2] => 0
[3,2,1,1] => 0
[3,1,1,1,1] => 0
[2,2,2,1] => 9
[2,2,1,1,1] => 3
[2,1,1,1,1,1] => 21
[1,1,1,1,1,1,1] => 351
[8] => 1
[7,1] => 1
[6,2] => 0
[6,1,1] => 0
[5,3] => 0
[5,2,1] => 1
[5,1,1,1] => 3
[4,4] => 1
[4,3,1] => 0
[4,2,2] => 1
[4,2,1,1] => 1
[4,1,1,1,1] => 9
[3,3,2] => 0
[3,3,1,1] => 0
[3,2,2,1] => 0
[3,2,1,1,1] => 0
[3,1,1,1,1,1] => 0
[2,2,2,2] => 33
[2,2,2,1,1] => 9
[2,2,1,1,1,1] => 9
[2,1,1,1,1,1,1] => 81
[1,1,1,1,1,1,1,1] => 1233
[9] => 0
[8,1] => 1
[7,2] => 1
[7,1,1] => 1
[6,3] => 0
[6,2,1] => 0
[6,1,1,1] => 0
[5,4] => 1
[5,3,1] => 0
[5,2,2] => 1
[5,2,1,1] => 1
[5,1,1,1,1] => 9
[4,4,1] => 1
[4,3,2] => 0
[4,3,1,1] => 0
[4,2,2,1] => 1
[4,2,1,1,1] => 3
[4,1,1,1,1,1] => 21
[3,3,3] => 18
[3,3,2,1] => 0
[3,3,1,1,1] => 0
[3,2,2,2] => 0
[3,2,2,1,1] => 0
[3,2,1,1,1,1] => 0
[3,1,1,1,1,1,1] => 0
[2,2,2,2,1] => 33
[2,2,2,1,1,1] => 27
[2,2,1,1,1,1,1] => 21
[2,1,1,1,1,1,1,1] => 351
[1,1,1,1,1,1,1,1,1] => 5769
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Description
The number of permutations whose cube equals a fixed permutation of given cycle type.
For example, the permutation $\pi=412365$ has cycle type $(4,2)$ and $234165$ is the unique permutation whose cube is $\pi$.
Code
@cached_function
def statistic_dict(n, k):
    d = {}
    for pi in Permutations(n):
        sigma = pi^k
        d[sigma] = d.get(sigma, 0) + 1
    return d

def statistic(la):
    n = la.size()
    d = statistic_dict(n, 3)
    sigma = standard_permutation(la)
    return d.get(sigma, 0)
Created
Mar 15, 2019 at 20:50 by Martin Rubey
Updated
Mar 15, 2019 at 20:50 by Martin Rubey