Identifier
Mp00033: to two-row standard tableauStandard tableaux
Mp00081: reading word permutationPermutations
Mp00086: Permutations first fundamental transformationPermutations
Mp00108: Permutations cycle type
Images
=>
Cc0005;cc-rep-0Cc0007;cc-rep-1Cc0002;cc-rep-4
[1,0]=>[[1],[2]]=>[2,1]=>[2,1]=>[2] [1,0,1,0]=>[[1,3],[2,4]]=>[2,4,1,3]=>[3,2,4,1]=>[3,1] [1,1,0,0]=>[[1,2],[3,4]]=>[3,4,1,2]=>[2,4,3,1]=>[3,1] [1,0,1,0,1,0]=>[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>[4,1,1] [1,0,1,1,0,0]=>[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>[4,1,1] [1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>[4,1,1] [1,1,0,1,0,0]=>[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>[4,1,1] [1,1,1,0,0,0]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[4,1,1] [1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[3,2,5,4,7,6,8,1]=>[5,1,1,1] [1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[2,4,3,6,5,8,7,1]=>[5,1,1,1] [1,1,0,1,1,0,0,0]=>[[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[2,4,3,5,8,6,7,1]=>[5,1,1,1] [1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[2,3,7,4,5,6,8,1]=>[5,1,1,1] [1,1,1,1,0,0,0,0]=>[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[2,3,4,8,5,6,7,1]=>[5,1,1,1]
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.
Map