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
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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.