Identifier
Values
=>
Cc0005;cc-rep-0 Cc0007;cc-rep
[1,0]=>[[1],[2]]=>0 [1,0,1,0]=>[[1,3],[2,4]]=>2 [1,1,0,0]=>[[1,2],[3,4]]=>0 [1,0,1,0,1,0]=>[[1,3,5],[2,4,6]]=>6 [1,0,1,1,0,0]=>[[1,3,4],[2,5,6]]=>2 [1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>4 [1,1,0,1,0,0]=>[[1,2,4],[3,5,6]]=>3 [1,1,1,0,0,0]=>[[1,2,3],[4,5,6]]=>0 [1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]]=>12 [1,0,1,0,1,1,0,0]=>[[1,3,5,6],[2,4,7,8]]=>6 [1,0,1,1,0,0,1,0]=>[[1,3,4,7],[2,5,6,8]]=>8 [1,0,1,1,0,1,0,0]=>[[1,3,4,6],[2,5,7,8]]=>7 [1,0,1,1,1,0,0,0]=>[[1,3,4,5],[2,6,7,8]]=>2 [1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]]=>10 [1,1,0,0,1,1,0,0]=>[[1,2,5,6],[3,4,7,8]]=>4 [1,1,0,1,0,0,1,0]=>[[1,2,4,7],[3,5,6,8]]=>9 [1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]]=>8 [1,1,0,1,1,0,0,0]=>[[1,2,4,5],[3,6,7,8]]=>3 [1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>6 [1,1,1,0,0,1,0,0]=>[[1,2,3,6],[4,5,7,8]]=>5 [1,1,1,0,1,0,0,0]=>[[1,2,3,5],[4,6,7,8]]=>4 [1,1,1,1,0,0,0,0]=>[[1,2,3,4],[5,6,7,8]]=>0
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Description
The major 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.