Identifier
-
Mp00033:
Dyck paths
—to two-row standard tableau⟶
Standard tableaux
St001698: Standard tableaux ⟶ ℤ
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]]=>4
[1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>2
[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]]=>10
[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]]=>9
[1,0,1,1,1,0,0,0]=>[[1,3,4,5],[2,6,7,8]]=>6
[1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]]=>6
[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]]=>7
[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]]=>5
[1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>2
[1,1,1,0,0,1,0,0]=>[[1,2,3,6],[4,5,7,8]]=>3
[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 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.
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.
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