Identifier
Values
=>
[1]=>0
[-1]=>1
[1,2]=>0
[1,-2]=>2
[-1,2]=>1
[-1,-2]=>3
[2,1]=>1
[2,-1]=>1
[-2,1]=>2
[-2,-1]=>2
[1,2,3]=>0
[1,2,-3]=>3
[1,-2,3]=>2
[1,-2,-3]=>5
[-1,2,3]=>1
[-1,2,-3]=>4
[-1,-2,3]=>3
[-1,-2,-3]=>6
[1,3,2]=>1
[1,3,-2]=>2
[1,-3,2]=>3
[1,-3,-2]=>4
[-1,3,2]=>2
[-1,3,-2]=>3
[-1,-3,2]=>4
[-1,-3,-2]=>5
[2,1,3]=>1
[2,1,-3]=>4
[2,-1,3]=>1
[2,-1,-3]=>4
[-2,1,3]=>2
[-2,1,-3]=>5
[-2,-1,3]=>2
[-2,-1,-3]=>5
[2,3,1]=>1
[2,3,-1]=>2
[2,-3,1]=>3
[2,-3,-1]=>4
[-2,3,1]=>2
[-2,3,-1]=>3
[-2,-3,1]=>4
[-2,-3,-1]=>5
[3,1,2]=>1
[3,1,-2]=>4
[3,-1,2]=>1
[3,-1,-2]=>4
[-3,1,2]=>2
[-3,1,-2]=>5
[-3,-1,2]=>2
[-3,-1,-2]=>5
[3,2,1]=>2
[3,2,-1]=>3
[3,-2,1]=>2
[3,-2,-1]=>3
[-3,2,1]=>3
[-3,2,-1]=>4
[-3,-2,1]=>3
[-3,-2,-1]=>4
[1,2,3,4]=>0
[1,2,3,-4]=>4
[1,2,-3,4]=>3
[1,2,-3,-4]=>7
[1,-2,3,4]=>2
[1,-2,3,-4]=>6
[1,-2,-3,4]=>5
[1,-2,-3,-4]=>9
[-1,2,3,4]=>1
[-1,2,3,-4]=>5
[-1,2,-3,4]=>4
[-1,2,-3,-4]=>8
[-1,-2,3,4]=>3
[-1,-2,3,-4]=>7
[-1,-2,-3,4]=>6
[-1,-2,-3,-4]=>10
[1,2,4,3]=>1
[1,2,4,-3]=>3
[1,2,-4,3]=>4
[1,2,-4,-3]=>6
[1,-2,4,3]=>3
[1,-2,4,-3]=>5
[1,-2,-4,3]=>6
[1,-2,-4,-3]=>8
[-1,2,4,3]=>2
[-1,2,4,-3]=>4
[-1,2,-4,3]=>5
[-1,2,-4,-3]=>7
[-1,-2,4,3]=>4
[-1,-2,4,-3]=>6
[-1,-2,-4,3]=>7
[-1,-2,-4,-3]=>9
[1,3,2,4]=>1
[1,3,2,-4]=>5
[1,3,-2,4]=>2
[1,3,-2,-4]=>6
[1,-3,2,4]=>3
[1,-3,2,-4]=>7
[1,-3,-2,4]=>4
[1,-3,-2,-4]=>8
[-1,3,2,4]=>2
[-1,3,2,-4]=>6
[-1,3,-2,4]=>3
[-1,3,-2,-4]=>7
[-1,-3,2,4]=>4
[-1,-3,2,-4]=>8
[-1,-3,-2,4]=>5
[-1,-3,-2,-4]=>9
[1,3,4,2]=>1
[1,3,4,-2]=>3
[1,3,-4,2]=>4
[1,3,-4,-2]=>6
[1,-3,4,2]=>3
[1,-3,4,-2]=>5
[1,-3,-4,2]=>6
[1,-3,-4,-2]=>8
[-1,3,4,2]=>2
[-1,3,4,-2]=>4
[-1,3,-4,2]=>5
[-1,3,-4,-2]=>7
[-1,-3,4,2]=>4
[-1,-3,4,-2]=>6
[-1,-3,-4,2]=>7
[-1,-3,-4,-2]=>9
[1,4,2,3]=>1
[1,4,2,-3]=>5
[1,4,-2,3]=>2
[1,4,-2,-3]=>6
[1,-4,2,3]=>3
[1,-4,2,-3]=>7
[1,-4,-2,3]=>4
[1,-4,-2,-3]=>8
[-1,4,2,3]=>2
[-1,4,2,-3]=>6
[-1,4,-2,3]=>3
[-1,4,-2,-3]=>7
[-1,-4,2,3]=>4
[-1,-4,2,-3]=>8
[-1,-4,-2,3]=>5
[-1,-4,-2,-3]=>9
[1,4,3,2]=>2
[1,4,3,-2]=>4
[1,4,-3,2]=>3
[1,4,-3,-2]=>5
[1,-4,3,2]=>4
[1,-4,3,-2]=>6
[1,-4,-3,2]=>5
[1,-4,-3,-2]=>7
[-1,4,3,2]=>3
[-1,4,3,-2]=>5
[-1,4,-3,2]=>4
[-1,4,-3,-2]=>6
[-1,-4,3,2]=>5
[-1,-4,3,-2]=>7
[-1,-4,-3,2]=>6
[-1,-4,-3,-2]=>8
[2,1,3,4]=>1
[2,1,3,-4]=>5
[2,1,-3,4]=>4
[2,1,-3,-4]=>8
[2,-1,3,4]=>1
[2,-1,3,-4]=>5
[2,-1,-3,4]=>4
[2,-1,-3,-4]=>8
[-2,1,3,4]=>2
[-2,1,3,-4]=>6
[-2,1,-3,4]=>5
[-2,1,-3,-4]=>9
[-2,-1,3,4]=>2
[-2,-1,3,-4]=>6
[-2,-1,-3,4]=>5
[-2,-1,-3,-4]=>9
[2,1,4,3]=>2
[2,1,4,-3]=>4
[2,1,-4,3]=>5
[2,1,-4,-3]=>7
[2,-1,4,3]=>2
[2,-1,4,-3]=>4
[2,-1,-4,3]=>5
[2,-1,-4,-3]=>7
[-2,1,4,3]=>3
[-2,1,4,-3]=>5
[-2,1,-4,3]=>6
[-2,1,-4,-3]=>8
[-2,-1,4,3]=>3
[-2,-1,4,-3]=>5
[-2,-1,-4,3]=>6
[-2,-1,-4,-3]=>8
[2,3,1,4]=>1
[2,3,1,-4]=>5
[2,3,-1,4]=>2
[2,3,-1,-4]=>6
[2,-3,1,4]=>3
[2,-3,1,-4]=>7
[2,-3,-1,4]=>4
[2,-3,-1,-4]=>8
[-2,3,1,4]=>2
[-2,3,1,-4]=>6
[-2,3,-1,4]=>3
[-2,3,-1,-4]=>7
[-2,-3,1,4]=>4
[-2,-3,1,-4]=>8
[-2,-3,-1,4]=>5
[-2,-3,-1,-4]=>9
[2,3,4,1]=>2
[2,3,4,-1]=>2
[2,3,-4,1]=>5
[2,3,-4,-1]=>5
[2,-3,4,1]=>4
[2,-3,4,-1]=>4
[2,-3,-4,1]=>7
[2,-3,-4,-1]=>7
[-2,3,4,1]=>3
[-2,3,4,-1]=>3
[-2,3,-4,1]=>6
[-2,3,-4,-1]=>6
[-2,-3,4,1]=>5
[-2,-3,4,-1]=>5
[-2,-3,-4,1]=>8
[-2,-3,-4,-1]=>8
[2,4,1,3]=>1
[2,4,1,-3]=>5
[2,4,-1,3]=>2
[2,4,-1,-3]=>6
[2,-4,1,3]=>3
[2,-4,1,-3]=>7
[2,-4,-1,3]=>4
[2,-4,-1,-3]=>8
[-2,4,1,3]=>2
[-2,4,1,-3]=>6
[-2,4,-1,3]=>3
[-2,4,-1,-3]=>7
[-2,-4,1,3]=>4
[-2,-4,1,-3]=>8
[-2,-4,-1,3]=>5
[-2,-4,-1,-3]=>9
[2,4,3,1]=>3
[2,4,3,-1]=>3
[2,4,-3,1]=>4
[2,4,-3,-1]=>4
[2,-4,3,1]=>5
[2,-4,3,-1]=>5
[2,-4,-3,1]=>6
[2,-4,-3,-1]=>6
[-2,4,3,1]=>4
[-2,4,3,-1]=>4
[-2,4,-3,1]=>5
[-2,4,-3,-1]=>5
[-2,-4,3,1]=>6
[-2,-4,3,-1]=>6
[-2,-4,-3,1]=>7
[-2,-4,-3,-1]=>7
[3,1,2,4]=>1
[3,1,2,-4]=>5
[3,1,-2,4]=>4
[3,1,-2,-4]=>8
[3,-1,2,4]=>1
[3,-1,2,-4]=>5
[3,-1,-2,4]=>4
[3,-1,-2,-4]=>8
[-3,1,2,4]=>2
[-3,1,2,-4]=>6
[-3,1,-2,4]=>5
[-3,1,-2,-4]=>9
[-3,-1,2,4]=>2
[-3,-1,2,-4]=>6
[-3,-1,-2,4]=>5
[-3,-1,-2,-4]=>9
[3,1,4,2]=>3
[3,1,4,-2]=>3
[3,1,-4,2]=>6
[3,1,-4,-2]=>6
[3,-1,4,2]=>3
[3,-1,4,-2]=>3
[3,-1,-4,2]=>6
[3,-1,-4,-2]=>6
[-3,1,4,2]=>4
[-3,1,4,-2]=>4
[-3,1,-4,2]=>7
[-3,1,-4,-2]=>7
[-3,-1,4,2]=>4
[-3,-1,4,-2]=>4
[-3,-1,-4,2]=>7
[-3,-1,-4,-2]=>7
[3,2,1,4]=>2
[3,2,1,-4]=>6
[3,2,-1,4]=>3
[3,2,-1,-4]=>7
[3,-2,1,4]=>2
[3,-2,1,-4]=>6
[3,-2,-1,4]=>3
[3,-2,-1,-4]=>7
[-3,2,1,4]=>3
[-3,2,1,-4]=>7
[-3,2,-1,4]=>4
[-3,2,-1,-4]=>8
[-3,-2,1,4]=>3
[-3,-2,1,-4]=>7
[-3,-2,-1,4]=>4
[-3,-2,-1,-4]=>8
[3,2,4,1]=>3
[3,2,4,-1]=>3
[3,2,-4,1]=>6
[3,2,-4,-1]=>6
[3,-2,4,1]=>3
[3,-2,4,-1]=>3
[3,-2,-4,1]=>6
[3,-2,-4,-1]=>6
[-3,2,4,1]=>4
[-3,2,4,-1]=>4
[-3,2,-4,1]=>7
[-3,2,-4,-1]=>7
[-3,-2,4,1]=>4
[-3,-2,4,-1]=>4
[-3,-2,-4,1]=>7
[-3,-2,-4,-1]=>7
[3,4,1,2]=>2
[3,4,1,-2]=>4
[3,4,-1,2]=>3
[3,4,-1,-2]=>5
[3,-4,1,2]=>4
[3,-4,1,-2]=>6
[3,-4,-1,2]=>5
[3,-4,-1,-2]=>7
[-3,4,1,2]=>3
[-3,4,1,-2]=>5
[-3,4,-1,2]=>4
[-3,4,-1,-2]=>6
[-3,-4,1,2]=>5
[-3,-4,1,-2]=>7
[-3,-4,-1,2]=>6
[-3,-4,-1,-2]=>8
[3,4,2,1]=>3
[3,4,2,-1]=>3
[3,4,-2,1]=>4
[3,4,-2,-1]=>4
[3,-4,2,1]=>5
[3,-4,2,-1]=>5
[3,-4,-2,1]=>6
[3,-4,-2,-1]=>6
[-3,4,2,1]=>4
[-3,4,2,-1]=>4
[-3,4,-2,1]=>5
[-3,4,-2,-1]=>5
[-3,-4,2,1]=>6
[-3,-4,2,-1]=>6
[-3,-4,-2,1]=>7
[-3,-4,-2,-1]=>7
[4,1,2,3]=>2
[4,1,2,-3]=>4
[4,1,-2,3]=>5
[4,1,-2,-3]=>7
[4,-1,2,3]=>2
[4,-1,2,-3]=>4
[4,-1,-2,3]=>5
[4,-1,-2,-3]=>7
[-4,1,2,3]=>3
[-4,1,2,-3]=>5
[-4,1,-2,3]=>6
[-4,1,-2,-3]=>8
[-4,-1,2,3]=>3
[-4,-1,2,-3]=>5
[-4,-1,-2,3]=>6
[-4,-1,-2,-3]=>8
[4,1,3,2]=>3
[4,1,3,-2]=>3
[4,1,-3,2]=>6
[4,1,-3,-2]=>6
[4,-1,3,2]=>3
[4,-1,3,-2]=>3
[4,-1,-3,2]=>6
[4,-1,-3,-2]=>6
[-4,1,3,2]=>4
[-4,1,3,-2]=>4
[-4,1,-3,2]=>7
[-4,1,-3,-2]=>7
[-4,-1,3,2]=>4
[-4,-1,3,-2]=>4
[-4,-1,-3,2]=>7
[-4,-1,-3,-2]=>7
[4,2,1,3]=>3
[4,2,1,-3]=>5
[4,2,-1,3]=>4
[4,2,-1,-3]=>6
[4,-2,1,3]=>3
[4,-2,1,-3]=>5
[4,-2,-1,3]=>4
[4,-2,-1,-3]=>6
[-4,2,1,3]=>4
[-4,2,1,-3]=>6
[-4,2,-1,3]=>5
[-4,2,-1,-3]=>7
[-4,-2,1,3]=>4
[-4,-2,1,-3]=>6
[-4,-2,-1,3]=>5
[-4,-2,-1,-3]=>7
[4,2,3,1]=>3
[4,2,3,-1]=>3
[4,2,-3,1]=>6
[4,2,-3,-1]=>6
[4,-2,3,1]=>3
[4,-2,3,-1]=>3
[4,-2,-3,1]=>6
[4,-2,-3,-1]=>6
[-4,2,3,1]=>4
[-4,2,3,-1]=>4
[-4,2,-3,1]=>7
[-4,2,-3,-1]=>7
[-4,-2,3,1]=>4
[-4,-2,3,-1]=>4
[-4,-2,-3,1]=>7
[-4,-2,-3,-1]=>7
[4,3,1,2]=>3
[4,3,1,-2]=>5
[4,3,-1,2]=>4
[4,3,-1,-2]=>6
[4,-3,1,2]=>3
[4,-3,1,-2]=>5
[4,-3,-1,2]=>4
[4,-3,-1,-2]=>6
[-4,3,1,2]=>4
[-4,3,1,-2]=>6
[-4,3,-1,2]=>5
[-4,3,-1,-2]=>7
[-4,-3,1,2]=>4
[-4,-3,1,-2]=>6
[-4,-3,-1,2]=>5
[-4,-3,-1,-2]=>7
[4,3,2,1]=>4
[4,3,2,-1]=>4
[4,3,-2,1]=>5
[4,3,-2,-1]=>5
[4,-3,2,1]=>4
[4,-3,2,-1]=>4
[4,-3,-2,1]=>5
[4,-3,-2,-1]=>5
[-4,3,2,1]=>5
[-4,3,2,-1]=>5
[-4,3,-2,1]=>6
[-4,3,-2,-1]=>6
[-4,-3,2,1]=>5
[-4,-3,2,-1]=>5
[-4,-3,-2,1]=>6
[-4,-3,-2,-1]=>6
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Description
The Stasinski-Voll length of a signed permutation.
The Stasinski-Voll length of a signed permutation $\sigma$ is
$$ L(\sigma) = \frac{1}{2} \#\{(i,j) ~\mid -n \leq i < j \leq n,~ i \not\equiv j \operatorname{mod} 2,~ \sigma(i) > \sigma(j)\}, $$
where $n$ is the size of $\sigma$.
The Stasinski-Voll length of a signed permutation $\sigma$ is
$$ L(\sigma) = \frac{1}{2} \#\{(i,j) ~\mid -n \leq i < j \leq n,~ i \not\equiv j \operatorname{mod} 2,~ \sigma(i) > \sigma(j)\}, $$
where $n$ is the size of $\sigma$.
References
[1] Stasinski, A., Voll, C. A new statistic on the hyperoctahedral groups arXiv:1303.0990
Code
def statistic(pi):
n = pi.parent().rank()
x = [-i for i in list(pi)]
x.reverse()
w = x + [0] + list(pi)
l = sum(1 for i in range(-n,n+1) for j in range(i+1,n+1) if w[i+n] > w[j+n] and i%2 != j%2)
return l/2
Created
Jul 22, 2022 at 11:45 by Dennis Jahn
Updated
Jul 22, 2022 at 11:45 by Dennis Jahn
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