Identifier
- St001536: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 0
[1,3,4,2] => 0
[1,4,2,3] => 0
[1,4,3,2] => 0
[2,1,3,4] => 0
[2,1,4,3] => 2
[2,3,1,4] => 0
[2,3,4,1] => 4
[2,4,1,3] => 0
[2,4,3,1] => 0
[3,1,2,4] => 0
[3,1,4,2] => 0
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 0
[4,2,1,3] => 0
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 2
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 0
[1,2,4,5,3] => 0
[1,2,5,3,4] => 0
[1,2,5,4,3] => 0
[1,3,2,4,5] => 0
[1,3,2,5,4] => 2
[1,3,4,2,5] => 0
[1,3,4,5,2] => 4
[1,3,5,2,4] => 0
[1,3,5,4,2] => 0
[1,4,2,3,5] => 0
[1,4,2,5,3] => 0
[1,4,3,2,5] => 0
[1,4,3,5,2] => 0
[1,4,5,2,3] => 0
[1,4,5,3,2] => 0
[1,5,2,3,4] => 0
[1,5,2,4,3] => 0
[1,5,3,2,4] => 0
[1,5,3,4,2] => 0
[1,5,4,2,3] => 0
[1,5,4,3,2] => 2
[2,1,3,4,5] => 0
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 4
[2,1,5,3,4] => 2
[2,1,5,4,3] => 2
[2,3,1,4,5] => 0
[2,3,1,5,4] => 4
[2,3,4,1,5] => 4
[2,3,4,5,1] => 10
[2,3,5,1,4] => 4
[2,3,5,4,1] => 4
[2,4,1,3,5] => 0
[2,4,1,5,3] => 2
[2,4,3,1,5] => 0
[2,4,3,5,1] => 4
[2,4,5,1,3] => 2
[2,4,5,3,1] => 4
[2,5,1,3,4] => 0
[2,5,1,4,3] => 0
[2,5,3,1,4] => 0
[2,5,3,4,1] => 0
[2,5,4,1,3] => 2
[2,5,4,3,1] => 4
[3,1,2,4,5] => 0
[3,1,2,5,4] => 2
[3,1,4,2,5] => 0
[3,1,4,5,2] => 4
[3,1,5,2,4] => 0
[3,1,5,4,2] => 0
[3,2,1,4,5] => 0
[3,2,1,5,4] => 2
[3,2,4,1,5] => 0
[3,2,4,5,1] => 4
[3,2,5,1,4] => 0
[3,2,5,4,1] => 0
[3,4,1,2,5] => 0
[3,4,1,5,2] => 2
[3,4,2,1,5] => 0
[3,4,2,5,1] => 4
[3,4,5,1,2] => 0
[3,4,5,2,1] => 2
[3,5,1,2,4] => 0
[3,5,1,4,2] => 0
>>> Load all 1200 entries. <<<
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of cyclic misalignments of a permutation.
The pair $(i,j)$ is a cyclic alignment of a permutation $\pi$ if $i, \pi(i), j, \pi(j)$ are cyclically ordered and all distinct, see Section 5 of [1].
The pair $(i,j)$ is a cyclic alignment of a permutation $\pi$ if $i, \pi(i), j, \pi(j)$ are cyclically ordered and all distinct, see Section 5 of [1].
References
[1] Postnikov, A. Total positivity, Grassmannians, and networks arXiv:math/0609764
Code
def in_cyclic_order(i, j, k, l):
return (i < j < k < l or
j < k < l < i or
k < l < i < j or
l < i < j < k)
def statistic(pi):
n = len(pi)
a = 0
for i, pi_i in enumerate(pi, 1):
for j, pi_j in enumerate(pi, 1):
if in_cyclic_order(i, pi_i, j, pi_j):
a += 1
return a
Created
May 09, 2020 at 22:17 by Martin Rubey
Updated
May 09, 2020 at 22:17 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!