Processing math: 100%

Identifier
Values
[1,0] => [[1],[2]] => [2,1] => [1,2] => 0
[1,0,1,0] => [[1,3],[2,4]] => [2,4,1,3] => [1,2,4,3] => 1
[1,1,0,0] => [[1,2],[3,4]] => [3,4,1,2] => [1,3,2,4] => 1
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [1,2,4,3,6,5] => 2
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [1,2,5,3,6,4] => 1
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [1,3,6,5,2,4] => 2
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [1,3,6,4,2,5] => 1
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [1,4,2,5,3,6] => 1
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [1,5,2,6,3,7,4,8] => 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 number of small exceedances.
This is the number of indices i such that πi=i+1.
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
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
to two-row standard tableau
Description
Return a standard tableau of shape (n,n) where n is the semilength of the Dyck path.
Given a Dyck path D, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.