Identifier
- St000222: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 1
[1,4,2,3] => 2
[1,4,3,2] => 2
[2,1,3,4] => 2
[2,1,4,3] => 2
[2,3,1,4] => 1
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,3,1] => 1
[3,1,2,4] => 2
[3,1,4,2] => 1
[3,2,1,4] => 2
[3,2,4,1] => 1
[3,4,1,2] => 0
[3,4,2,1] => 1
[4,1,2,3] => 0
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 1
[4,3,2,1] => 2
[1,2,3,4,5] => 0
[1,2,3,5,4] => 3
[1,2,4,3,5] => 3
[1,2,4,5,3] => 2
[1,2,5,3,4] => 4
[1,2,5,4,3] => 3
[1,3,2,4,5] => 3
[1,3,2,5,4] => 4
[1,3,4,2,5] => 2
[1,3,4,5,2] => 1
[1,3,5,2,4] => 3
[1,3,5,4,2] => 2
[1,4,2,3,5] => 4
[1,4,2,5,3] => 3
[1,4,3,2,5] => 3
[1,4,3,5,2] => 2
[1,4,5,2,3] => 2
[1,4,5,3,2] => 3
[1,5,2,3,4] => 3
[1,5,2,4,3] => 4
[1,5,3,2,4] => 4
[1,5,3,4,2] => 3
[1,5,4,2,3] => 3
[1,5,4,3,2] => 4
[2,1,3,4,5] => 3
[2,1,3,5,4] => 4
[2,1,4,3,5] => 4
[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] => 1
[2,3,4,5,1] => 0
[2,3,5,1,4] => 2
[2,3,5,4,1] => 1
[2,4,1,3,5] => 3
[2,4,1,5,3] => 2
[2,4,3,1,5] => 2
[2,4,3,5,1] => 1
[2,4,5,1,3] => 1
[2,4,5,3,1] => 2
[2,5,1,3,4] => 2
[2,5,1,4,3] => 3
[2,5,3,1,4] => 3
[2,5,3,4,1] => 2
[2,5,4,1,3] => 2
[2,5,4,3,1] => 3
[3,1,2,4,5] => 4
[3,1,2,5,4] => 3
[3,1,4,2,5] => 3
[3,1,4,5,2] => 2
[3,1,5,2,4] => 2
[3,1,5,4,2] => 3
[3,2,1,4,5] => 3
[3,2,1,5,4] => 4
[3,2,4,1,5] => 2
[3,2,4,5,1] => 1
[3,2,5,1,4] => 3
[3,2,5,4,1] => 2
[3,4,1,2,5] => 2
[3,4,1,5,2] => 1
[3,4,2,1,5] => 3
[3,4,2,5,1] => 2
[3,4,5,1,2] => 0
[3,4,5,2,1] => 1
[3,5,1,2,4] => 1
[3,5,1,4,2] => 2
>>> Load all 873 entries. <<<
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Description
The number of alignments in the permutation.
References
[1] Corteel, S. Crossings and alignments of permutations MathSciNet:2290808
Code
def statistic(pi):
al = 0
n = len(pi)
for i in range(n):
for j in range(n):
if j < i < pi[i] < pi[j] or pi[j] < pi[i] <= i < j or j+1 <= pi[j] < pi[i] < i+1 or pi[i] < i+1 < j+1 <= pi[j]:
al = al+1
return al
Created
Sep 26, 2014 at 11:37 by Martin Rubey
Updated
Nov 16, 2017 at 11:40 by Martin Rubey
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