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Identifier

St001555: Signed permutations ⟶ ℤ

Values

[1] => 1

[-1] => 2

[1,2] => 1

[1,-2] => 2

[-1,2] => 2

[-1,-2] => 2

[2,1] => 2

[2,-1] => 4

[-2,1] => 4

[-2,-1] => 2

[1,2,3] => 1

[1,2,-3] => 2

[1,-2,3] => 2

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

[-1,2,3] => 2

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

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

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

[1,3,2] => 2

[1,3,-2] => 4

[1,-3,2] => 4

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

[-1,3,2] => 2

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

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

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

[2,1,3] => 2

[2,1,-3] => 2

[2,-1,3] => 4

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

[-2,1,3] => 4

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

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

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

[2,3,1] => 3

[2,3,-1] => 6

[2,-3,1] => 6

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

[-2,3,1] => 6

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

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

[-2,-3,-1] => 6

[3,1,2] => 3

[3,1,-2] => 6

[3,-1,2] => 6

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

[-3,1,2] => 6

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

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

[-3,-1,-2] => 6

[3,2,1] => 2

[3,2,-1] => 4

[3,-2,1] => 2

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

[-3,2,1] => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The order of a signed permutation.

Code

def statistic(pi):
    n = len(list(pi))
    order = 1
    tau = pi
    while list(tau) != [1 .. n]:
        tau *= pi
        order += 1
    return order

Created

Jun 24, 2020 at 10:52 by Christian Stump

Updated

Jun 24, 2020 at 10:52 by Christian Stump