Identifier
Values
[1] => [1,0] => [1,0] => [2,1] => 0
[1,1] => [1,0,1,0] => [1,1,0,0] => [2,3,1] => 0
[2] => [1,1,0,0] => [1,0,1,0] => [3,1,2] => 0
[1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => [4,3,1,2] => 0
[1,2] => [1,0,1,1,0,0] => [1,1,1,0,0,0] => [2,3,4,1] => 0
[2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => [3,1,4,2] => 0
[3] => [1,1,1,0,0,0] => [1,1,0,0,1,0] => [2,4,1,3] => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 0
[1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [4,3,1,5,2] => 0
[1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 0
[1,3] => [1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
[2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 0
[2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 0
[3,1] => [1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 0
[4] => [1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 0
[1,1,1,1,1] => [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] => 0
[1,1,1,2] => [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] => 0
[1,1,2,1] => [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] => 0
[1,1,3] => [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] => 0
[1,2,1,1] => [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] => 0
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => 0
[1,3,1] => [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] => 0
[1,4] => [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] => 0
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 0
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => 0
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 0
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 0
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 0
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 0
[5] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 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
Number of occurrences of the patterns 41352,42351,51342,52341 in a permutation.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
inverse promotion
Description
The inverse promotion of a Dyck path.
This is the bijection obtained by applying the inverse of Schützenberger's promotion to the corresponding two rowed standard Young tableau.