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Identifier

St001427: Signed permutations ⟶ ℤ

Values

[1] => 0

[-1] => 1

[1,2] => 0

[1,-2] => 1

[-1,2] => 1

[-1,-2] => 2

[2,1] => 1

[2,-1] => 1

[-2,1] => 1

[-2,-1] => 1

[1,2,3] => 0

[1,2,-3] => 1

[1,-2,3] => 1

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

[-1,2,3] => 1

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

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

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

[1,3,2] => 1

[1,3,-2] => 1

[1,-3,2] => 1

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

[-1,3,2] => 2

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

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

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

[2,1,3] => 1

[2,1,-3] => 2

[2,-1,3] => 1

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

[-2,1,3] => 1

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

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

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

[2,3,1] => 1

[2,3,-1] => 1

[2,-3,1] => 1

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

[-2,3,1] => 2

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

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

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

[3,1,2] => 1

[3,1,-2] => 2

[3,-1,2] => 1

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

[-3,1,2] => 1

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

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

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

[3,2,1] => 2

[3,2,-1] => 2

[3,-2,1] => 1

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

[-3,2,1] => 2

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

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

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

[1,2,3,4] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of descents of a signed permutation.
A descent of a signed permutation $\sigma$ of length $n$ is an index $0 \leq i < n$ such that $\sigma(i) > \sigma(i+1)$, setting $\sigma(0) = 0$.

Code

def statistic(pi):
    pi = [0] + list(pi)
    return sum(1 for i in range(len(pi)-1) if pi[i] > pi[i+1])

Created

Jun 21, 2019 at 13:52 by Christian Stump

Updated

Jun 30, 2023 at 14:25 by Martin Rubey