Identifier
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [2,3,1] => [2,3,1] => 0
[2,1,3] => [1,3,2] => [2,3,1] => [2,3,1] => 0
[2,3,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [2,3,4,1] => [2,3,4,1] => 0
[1,3,2,4] => [1,3,2,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,3,4,2] => [1,3,4,2] => [2,4,1,3] => [2,4,1,3] => 0
[1,4,2,3] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[1,4,3,2] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[2,1,3,4] => [1,3,4,2] => [2,4,1,3] => [2,4,1,3] => 0
[2,1,4,3] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[2,3,1,4] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [2,3,1,4] => [2,3,1,4] => 1
[2,4,3,1] => [1,2,4,3] => [2,3,4,1] => [2,3,4,1] => 0
[3,1,2,4] => [1,2,4,3] => [2,3,4,1] => [2,3,4,1] => 0
[3,1,4,2] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[3,2,1,4] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[3,2,4,1] => [1,2,4,3] => [2,3,4,1] => [2,3,4,1] => 0
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [2,3,1,4] => [2,3,1,4] => 1
[4,2,1,3] => [1,3,2,4] => [2,3,1,4] => [2,3,1,4] => 1
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,4,5,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,4,5,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,1,2,3,4] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,2,3,4,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,3,4,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,3,4,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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 alignments of type NE of a signed permutation.
An alignment of type NE of a signed permutation $\pi\in\mathfrak H_n$ is a pair $1 \leq i, j\leq n$ such that $\pi(i) < i < j \leq \pi(j)$.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.