Identifier
Values
[1] => [1,0,1,0] => [1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => 3
[2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => 3
[1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => 5
[2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => 8
[] => [] => [1,0] => [[1],[2]] => 0
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Description
The comajor index of a standard tableau minus the weighted size of its shape.
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.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.