Identifier
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,2,3] => [1,2,3] => 0
[2,1,3] => [2,1,3] => [1,2,3] => [1,2,3] => 0
[2,3,1] => [3,2,1] => [1,3,2] => [1,2,3] => 0
[3,1,2] => [3,2,1] => [1,3,2] => [1,2,3] => 0
[3,2,1] => [3,2,1] => [1,3,2] => [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] => [1,2,3,4] => [1,2,3,4] => 0
[1,3,2,4] => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,3,4,2] => [1,4,3,2] => [1,2,4,3] => [1,2,3,4] => 0
[1,4,2,3] => [1,4,3,2] => [1,2,4,3] => [1,2,3,4] => 0
[1,4,3,2] => [1,4,3,2] => [1,2,4,3] => [1,2,3,4] => 0
[2,1,3,4] => [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,1,4,3] => [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
[2,3,1,4] => [3,2,1,4] => [1,3,2,4] => [1,2,3,4] => 0
[2,3,4,1] => [4,2,3,1] => [1,4,2,3] => [1,2,4,3] => 1
[2,4,1,3] => [3,4,1,2] => [1,3,2,4] => [1,2,3,4] => 0
[2,4,3,1] => [4,3,2,1] => [1,4,2,3] => [1,2,4,3] => 1
[3,1,2,4] => [3,2,1,4] => [1,3,2,4] => [1,2,3,4] => 0
[3,1,4,2] => [4,2,3,1] => [1,4,2,3] => [1,2,4,3] => 1
[3,2,1,4] => [3,2,1,4] => [1,3,2,4] => [1,2,3,4] => 0
[3,2,4,1] => [4,2,3,1] => [1,4,2,3] => [1,2,4,3] => 1
[3,4,1,2] => [4,3,2,1] => [1,4,2,3] => [1,2,4,3] => 1
[3,4,2,1] => [4,3,2,1] => [1,4,2,3] => [1,2,4,3] => 1
[4,1,2,3] => [4,2,3,1] => [1,4,2,3] => [1,2,4,3] => 1
[4,1,3,2] => [4,2,3,1] => [1,4,2,3] => [1,2,4,3] => 1
[4,2,1,3] => [4,3,2,1] => [1,4,2,3] => [1,2,4,3] => 1
[4,2,3,1] => [4,3,2,1] => [1,4,2,3] => [1,2,4,3] => 1
[4,3,1,2] => [4,3,2,1] => [1,4,2,3] => [1,2,4,3] => 1
[4,3,2,1] => [4,3,2,1] => [1,4,2,3] => [1,2,4,3] => 1
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 Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.