Identifier
- St000495: Permutations ⟶ ℤ
Values
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 3
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 2
[2,4,1,3] => 3
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 3
[3,4,2,1] => 4
[4,1,2,3] => 2
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 4
[4,3,1,2] => 4
[4,3,2,1] => 5
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 3
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 2
[1,3,5,2,4] => 3
[1,3,5,4,2] => 3
[1,4,2,3,5] => 2
[1,4,2,5,3] => 2
[1,4,3,2,5] => 3
[1,4,3,5,2] => 3
[1,4,5,2,3] => 3
[1,4,5,3,2] => 4
[1,5,2,3,4] => 2
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 4
[1,5,4,2,3] => 4
[1,5,4,3,2] => 5
[2,1,3,4,5] => 1
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 3
[2,1,5,3,4] => 3
[2,1,5,4,3] => 4
[2,3,1,4,5] => 2
[2,3,1,5,4] => 3
[2,3,4,1,5] => 2
[2,3,4,5,1] => 2
[2,3,5,1,4] => 3
[2,3,5,4,1] => 3
[2,4,1,3,5] => 3
[2,4,1,5,3] => 3
[2,4,3,1,5] => 3
[2,4,3,5,1] => 3
[2,4,5,1,3] => 3
[2,4,5,3,1] => 4
[2,5,1,3,4] => 3
[2,5,1,4,3] => 4
[2,5,3,1,4] => 3
[2,5,3,4,1] => 4
[2,5,4,1,3] => 4
[2,5,4,3,1] => 5
[3,1,2,4,5] => 2
[3,1,2,5,4] => 3
[3,1,4,2,5] => 2
[3,1,4,5,2] => 3
[3,1,5,2,4] => 3
[3,1,5,4,2] => 4
[3,2,1,4,5] => 3
[3,2,1,5,4] => 4
[3,2,4,1,5] => 3
[3,2,4,5,1] => 3
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 3
[3,4,1,5,2] => 3
[3,4,2,1,5] => 4
[3,4,2,5,1] => 4
[3,4,5,1,2] => 3
[3,4,5,2,1] => 4
[3,5,1,2,4] => 3
[3,5,1,4,2] => 4
[3,5,2,1,4] => 4
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Description
The number of inversions of distance at most 2 of a permutation.
An inversion of a permutation $\pi$ is a pair $i < j$ such that $\sigma(i) > \sigma(j)$. Let $j-i$ be the distance of such an inversion. Then inversions of distance at most 1 are then exactly the descents of $\pi$, see St000021The number of descents of a permutation.. This statistic counts the number of inversions of distance at most 2.
An inversion of a permutation $\pi$ is a pair $i < j$ such that $\sigma(i) > \sigma(j)$. Let $j-i$ be the distance of such an inversion. Then inversions of distance at most 1 are then exactly the descents of $\pi$, see St000021The number of descents of a permutation.. This statistic counts the number of inversions of distance at most 2.
Code
def statistic(pi):
k = 2
return sum( 1 for i,j in pi.inversions() if j-i <= k )
Created
May 18, 2016 at 11:59 by Christian Stump
Updated
May 18, 2016 at 11:59 by Christian Stump
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