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Identifier
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
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Description
The number of descents of a signed permutation.
A descent of a signed permutation $\sigma$ of length $n$ is the number of indices $0 \leq i < n$ such that $\sigma(i) > \sigma(i+1)$ where one considers $\sigma(0) = 0$.
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 21, 2019 at 13:52 by Christian Stump