Identifier
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [2,1] => [2,1] => 0
[2,1] => [1,2] => [2,1] => [2,1] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,3,2] => [1,3,2] => [2,1,3] => [2,1,3] => 0
[2,1,3] => [1,3,2] => [2,1,3] => [2,1,3] => 0
[2,3,1] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[3,1,2] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[3,2,1] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 0
[1,2,4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 0
[1,3,2,4] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1] => 0
[1,3,4,2] => [1,3,4,2] => [2,1,3,4] => [2,1,3,4] => 0
[1,4,2,3] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 1
[1,4,3,2] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 1
[2,1,3,4] => [1,3,4,2] => [2,1,3,4] => [2,1,3,4] => 0
[2,1,4,3] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 1
[2,3,1,4] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 1
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 0
[2,4,1,3] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1] => 0
[2,4,3,1] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 0
[3,1,2,4] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 0
[3,1,4,2] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 1
[3,2,1,4] => [1,4,2,3] => [2,4,1,3] => [2,4,1,3] => 1
[3,2,4,1] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 0
[3,4,1,2] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 0
[3,4,2,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 0
[4,1,2,3] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 0
[4,1,3,2] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1] => 0
[4,2,1,3] => [1,3,2,4] => [2,4,3,1] => [2,4,3,1] => 0
[4,2,3,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 0
[4,3,1,2] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 0
[4,3,2,1] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 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 EN of a signed permutation.
An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold:
  • $-i < 0 < -\pi(i) < \pi(j) < j$
  • $i \leq\pi(i) < \pi(j) < j$.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.