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
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.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.