Identifier
Values
[1] => [1,0] => [1,0] => [[1],[2]] => 1
[1,1] => [1,1,0,0] => [1,0,1,0] => [[1,3],[2,4]] => 2
[1,2] => [1,0,1,0] => [1,1,0,0] => [[1,2],[3,4]] => 1
[2,1] => [1,0,1,0] => [1,1,0,0] => [[1,2],[3,4]] => 1
[1,1,1] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 3
[1,1,2] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => 2
[1,2,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => 2
[2,1,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => 2
[1,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => 2
[1,3,1] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => 2
[3,1,1] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => 2
[1,2,2] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => 1
[2,1,2] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => 1
[2,2,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => 1
[1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => 1
[1,3,2] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => 1
[2,1,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => 1
[2,3,1] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => 1
[3,1,2] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => 1
[3,2,1] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => 1
[1,1,1,1] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 4
[1,1,1,2] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 3
[1,1,2,1] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 3
[1,2,1,1] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 3
[2,1,1,1] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 3
[1,1,1,3] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 3
[1,1,3,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 3
[1,3,1,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 3
[3,1,1,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 3
[1,1,1,4] => [1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 3
[1,1,4,1] => [1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 3
[1,4,1,1] => [1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 3
[4,1,1,1] => [1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 3
[1,1,2,2] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 2
[1,2,1,2] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 2
[1,2,2,1] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 2
[2,1,1,2] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 2
[2,1,2,1] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 2
[2,2,1,1] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 2
[1,1,2,3] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[1,1,3,2] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[1,2,1,3] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[1,2,3,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[1,3,1,2] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[1,3,2,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[2,1,1,3] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[2,1,3,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[2,3,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[3,1,1,2] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[3,1,2,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[3,2,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[1,1,2,4] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[1,1,4,2] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[1,2,1,4] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[1,2,4,1] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[1,4,1,2] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[1,4,2,1] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[2,1,1,4] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[2,1,4,1] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[2,4,1,1] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[4,1,1,2] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[4,1,2,1] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[4,2,1,1] => [1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[1,1,3,3] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 2
[1,3,1,3] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 2
[1,3,3,1] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 2
[3,1,1,3] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 2
[3,1,3,1] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 2
[3,3,1,1] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 2
[1,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[1,1,4,3] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[1,3,1,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[1,3,4,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[1,4,1,3] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[1,4,3,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[3,1,1,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[3,1,4,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[3,4,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[4,1,1,3] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[4,1,3,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[4,3,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[1,2,2,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => 1
[2,1,2,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => 1
[2,2,1,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => 1
[2,2,2,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => 1
[1,2,2,3] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[1,2,3,2] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[1,3,2,2] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[2,1,2,3] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[2,1,3,2] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[2,2,1,3] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[2,2,3,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[2,3,1,2] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[2,3,2,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[3,1,2,2] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[3,2,1,2] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[3,2,2,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 1
[1,2,2,4] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[1,2,4,2] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[1,4,2,2] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[2,1,2,4] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
>>> Load all 145 entries. <<<
[2,1,4,2] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[2,2,1,4] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[2,2,4,1] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[2,4,1,2] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[2,4,2,1] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[4,1,2,2] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[4,2,1,2] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[4,2,2,1] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 1
[1,2,3,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[1,3,2,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[1,3,3,2] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[2,1,3,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[2,3,1,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[2,3,3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[3,1,2,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[3,1,3,2] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[3,2,1,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[3,2,3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[3,3,1,2] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[3,3,2,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => 1
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[1,2,4,3] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[1,3,2,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[1,3,4,2] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[1,4,2,3] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[1,4,3,2] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[2,1,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[2,1,4,3] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[2,3,1,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[2,3,4,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[2,4,1,3] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[2,4,3,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[3,1,2,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[3,1,4,2] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[3,2,1,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[3,2,4,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[3,4,1,2] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[3,4,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[4,1,2,3] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[4,1,3,2] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[4,2,1,3] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[4,2,3,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[4,3,1,2] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
[4,3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => 1
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Description
The number of factors of a standard tableaux under concatenation.
The concatenation of two standard Young tableaux $T_1$ and $T_2$ is obtained by adding the largest entry of $T_1$ to each entry of $T_2$, and then appending the rows of the result to $T_1$, see [1, dfn 2.10].
This statistic returns the maximal number of standard tableaux such that their concatenation is the given tableau.
Map
to Dyck path
Description
Sends a parking function to its support Dyck word.
Map
decomposition reverse
Description
This map is recursively defined as follows.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.
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.