Identifier
-
Mp00033:
Dyck paths
—to two-row standard tableau⟶
Standard tableaux
Mp00226: Standard tableaux —row-to-column-descents⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000237: Permutations ⟶ ℤ
Values
[1,0] => [[1],[2]] => [[1],[2]] => [2,1] => 1
[1,0,1,0] => [[1,3],[2,4]] => [[1,2],[3,4]] => [3,4,1,2] => 0
[1,1,0,0] => [[1,2],[3,4]] => [[1,3],[2,4]] => [2,4,1,3] => 1
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 0
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 0
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 1
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 0
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 1
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => 0
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => 0
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [[1,2,5,6],[3,4,7,8]] => [3,4,7,8,1,2,5,6] => 0
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => 0
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => 0
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [[1,3,4,6],[2,5,7,8]] => [2,5,7,8,1,3,4,6] => 1
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [[1,3,4,7],[2,5,6,8]] => [2,5,6,8,1,3,4,7] => 1
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => 0
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [[1,2,3,5],[4,6,7,8]] => [4,6,7,8,1,2,3,5] => 0
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => 0
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => 1
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [[1,3,4,5],[2,6,7,8]] => [2,6,7,8,1,3,4,5] => 1
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 0
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => 1
[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => [[1,2,4,6,8],[3,5,7,9,10]] => [3,5,7,9,10,1,2,4,6,8] => 0
[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => [[1,2,4,6,9],[3,5,7,8,10]] => [3,5,7,8,10,1,2,4,6,9] => 0
[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => [[1,2,4,7,8],[3,5,6,9,10]] => [3,5,6,9,10,1,2,4,7,8] => 0
[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => [[1,2,4,6,7],[3,5,8,9,10]] => [3,5,8,9,10,1,2,4,6,7] => 0
[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => [[1,2,4,7,9],[3,5,6,8,10]] => [3,5,6,8,10,1,2,4,7,9] => 0
[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => [[1,2,5,6,8],[3,4,7,9,10]] => [3,4,7,9,10,1,2,5,6,8] => 0
[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => [[1,2,5,6,9],[3,4,7,8,10]] => [3,4,7,8,10,1,2,5,6,9] => 0
[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => [[1,2,4,5,8],[3,6,7,9,10]] => [3,6,7,9,10,1,2,4,5,8] => 0
[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => [[1,2,4,5,7],[3,6,8,9,10]] => [3,6,8,9,10,1,2,4,5,7] => 0
[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => [[1,2,4,5,9],[3,6,7,8,10]] => [3,6,7,8,10,1,2,4,5,9] => 0
[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => [[1,2,5,7,8],[3,4,6,9,10]] => [3,4,6,9,10,1,2,5,7,8] => 0
[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => [[1,2,5,6,7],[3,4,8,9,10]] => [3,4,8,9,10,1,2,5,6,7] => 0
[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => [[1,2,4,5,6],[3,7,8,9,10]] => [3,7,8,9,10,1,2,4,5,6] => 0
[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => [[1,2,5,7,9],[3,4,6,8,10]] => [3,4,6,8,10,1,2,5,7,9] => 0
[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => [[1,3,4,6,8],[2,5,7,9,10]] => [2,5,7,9,10,1,3,4,6,8] => 1
[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => [[1,3,4,6,9],[2,5,7,8,10]] => [2,5,7,8,10,1,3,4,6,9] => 1
[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => [[1,3,4,7,8],[2,5,6,9,10]] => [2,5,6,9,10,1,3,4,7,8] => 1
[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => [[1,3,4,6,7],[2,5,8,9,10]] => [2,5,8,9,10,1,3,4,6,7] => 1
[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => [[1,3,4,7,9],[2,5,6,8,10]] => [2,5,6,8,10,1,3,4,7,9] => 1
[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => [[1,2,3,6,8],[4,5,7,9,10]] => [4,5,7,9,10,1,2,3,6,8] => 0
[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => [[1,2,3,6,9],[4,5,7,8,10]] => [4,5,7,8,10,1,2,3,6,9] => 0
[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => [[1,2,3,5,8],[4,6,7,9,10]] => [4,6,7,9,10,1,2,3,5,8] => 0
[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => [[1,2,3,5,7],[4,6,8,9,10]] => [4,6,8,9,10,1,2,3,5,7] => 0
[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => [[1,2,3,5,9],[4,6,7,8,10]] => [4,6,7,8,10,1,2,3,5,9] => 0
[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => [[1,2,3,7,8],[4,5,6,9,10]] => [4,5,6,9,10,1,2,3,7,8] => 0
[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => [[1,2,3,6,7],[4,5,8,9,10]] => [4,5,8,9,10,1,2,3,6,7] => 0
[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => [[1,2,3,5,6],[4,7,8,9,10]] => [4,7,8,9,10,1,2,3,5,6] => 0
[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => [[1,2,3,7,9],[4,5,6,8,10]] => [4,5,6,8,10,1,2,3,7,9] => 0
[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => [[1,3,5,6,8],[2,4,7,9,10]] => [2,4,7,9,10,1,3,5,6,8] => 1
[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => [[1,3,5,6,9],[2,4,7,8,10]] => [2,4,7,8,10,1,3,5,6,9] => 1
[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => [[1,3,4,5,8],[2,6,7,9,10]] => [2,6,7,9,10,1,3,4,5,8] => 1
[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => [[1,3,4,5,7],[2,6,8,9,10]] => [2,6,8,9,10,1,3,4,5,7] => 1
[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => [[1,3,4,5,9],[2,6,7,8,10]] => [2,6,7,8,10,1,3,4,5,9] => 1
[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => [[1,2,3,4,8],[5,6,7,9,10]] => [5,6,7,9,10,1,2,3,4,8] => 0
[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => [[1,2,3,4,7],[5,6,8,9,10]] => [5,6,8,9,10,1,2,3,4,7] => 0
[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => [[1,2,3,4,6],[5,7,8,9,10]] => [5,7,8,9,10,1,2,3,4,6] => 0
[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => [[1,2,3,4,9],[5,6,7,8,10]] => [5,6,7,8,10,1,2,3,4,9] => 0
[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => [[1,3,5,7,8],[2,4,6,9,10]] => [2,4,6,9,10,1,3,5,7,8] => 1
[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => [[1,3,5,6,7],[2,4,8,9,10]] => [2,4,8,9,10,1,3,5,6,7] => 1
[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => [[1,3,4,5,6],[2,7,8,9,10]] => [2,7,8,9,10,1,3,4,5,6] => 1
[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,3,5,7,9],[2,4,6,8,10]] => [2,4,6,8,10,1,3,5,7,9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => [3,5,7,9,11,12,1,2,4,6,8,10] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => [3,5,7,9,10,12,1,2,4,6,8,11] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => [3,5,7,8,11,12,1,2,4,6,9,10] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => [3,5,7,10,11,12,1,2,4,6,8,9] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => [3,5,7,8,10,12,1,2,4,6,9,11] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => [3,5,6,9,11,12,1,2,4,7,8,10] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => [3,5,6,9,10,12,1,2,4,7,8,11] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => [3,5,8,9,11,12,1,2,4,6,7,10] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => [3,5,8,10,11,12,1,2,4,6,7,9] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => [3,5,8,9,10,12,1,2,4,6,7,11] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => [3,5,6,8,11,12,1,2,4,7,9,10] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => [3,5,6,10,11,12,1,2,4,7,8,9] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => [3,5,9,10,11,12,1,2,4,6,7,8] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => [3,5,6,8,10,12,1,2,4,7,9,11] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => [3,4,7,9,11,12,1,2,5,6,8,10] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => [3,4,7,9,10,12,1,2,5,6,8,11] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => [3,4,7,8,11,12,1,2,5,6,9,10] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => [3,4,7,10,11,12,1,2,5,6,8,9] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => [3,4,7,8,10,12,1,2,5,6,9,11] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => [3,6,7,9,11,12,1,2,4,5,8,10] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => [3,6,7,9,10,12,1,2,4,5,8,11] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => [3,6,8,9,11,12,1,2,4,5,7,10] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => [3,6,8,10,11,12,1,2,4,5,7,9] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => [3,6,8,9,10,12,1,2,4,5,7,11] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => [3,6,7,8,11,12,1,2,4,5,9,10] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => [3,6,7,10,11,12,1,2,4,5,8,9] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => [3,6,9,10,11,12,1,2,4,5,7,8] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => [3,6,7,8,10,12,1,2,4,5,9,11] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => [3,4,6,9,11,12,1,2,5,7,8,10] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => [3,4,6,9,10,12,1,2,5,7,8,11] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => [3,4,8,9,11,12,1,2,5,6,7,10] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => [3,4,8,10,11,12,1,2,5,6,7,9] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => [3,4,8,9,10,12,1,2,5,6,7,11] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => [3,7,8,9,11,12,1,2,4,5,6,10] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => [3,7,8,10,11,12,1,2,4,5,6,9] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => [3,7,9,10,11,12,1,2,4,5,6,8] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => [3,7,8,9,10,12,1,2,4,5,6,11] => 0
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Description
The number of small exceedances.
This is the number of indices $i$ such that $\pi_i=i+1$.
This is the number of indices $i$ such that $\pi_i=i+1$.
Map
row-to-column-descents
Description
Return a standard tableau whose column descent set equals the row descent set of the original tableau.
A column descent in a standard tableau is an entry $i$ such that $i+1$ appears in a column to the left of the cell containing $i$, in English notation.
A row descent is an entry $i$ such that $i+1$ appears in a row above of the cell containing $i$.
A column descent in a standard tableau is an entry $i$ such that $i+1$ appears in a column to the left of the cell containing $i$, in English notation.
A row descent is an entry $i$ such that $i+1$ appears in a row above of the cell containing $i$.
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.
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.
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.
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