Identifier
Values
[1,0] => [1,1,0,0] => [2,3,1] => [3,2,1] => 0
[1,0,1,0] => [1,1,0,1,0,0] => [4,3,1,2] => [4,3,2,1] => 0
[1,1,0,0] => [1,1,1,0,0,0] => [2,3,4,1] => [4,2,3,1] => 0
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [5,4,3,2,1] => 0
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [5,3,2,4,1] => 0
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,5,3,1,2] => 0
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [5,4,3,2,1] => 0
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => 0
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [6,5,3,4,2,1] => 0
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [6,4,3,2,5,1] => 0
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [6,5,3,4,2,1] => 0
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [6,5,3,4,2,1] => 0
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [6,3,2,4,5,1] => 0
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [4,6,5,1,3,2] => 0
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [4,6,3,1,5,2] => 0
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [6,5,4,3,2,1] => 0
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [6,5,4,3,2,1] => 0
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [6,4,3,2,5,1] => 0
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,2,6,4,1,3] => 1
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [5,6,4,3,1,2] => 0
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [6,5,4,3,2,1] => 0
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 0
[] => [1,0] => [2,1] => [2,1] => 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 occurrences of 14-2-3 or 14-3-2.
The number of permutations avoiding both of these patterns is the case $k=2$ of the third item in Corollary 34 of [1].
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 $\pi = \pi^{-1}$.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.