Identifier
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Images
=>
Cc0005;cc-rep-0Cc0007;cc-rep-1Cc0007;cc-rep-4
[1,0]=>[[1],[2]]=>[2,1]=>[1,2]=>[[1,2]] [1,0,1,0]=>[[1,3],[2,4]]=>[2,4,1,3]=>[3,1,4,2]=>[[1,3],[2,4]] [1,1,0,0]=>[[1,2],[3,4]]=>[3,4,1,2]=>[2,1,4,3]=>[[1,3],[2,4]] [1,0,1,0,1,0]=>[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[[1,4],[2,5],[3,6]] [1,0,1,1,0,0]=>[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>[[1,4],[2,5],[3,6]] [1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>[[1,4],[2,5],[3,6]] [1,1,0,1,0,0]=>[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[[1,4],[2,5],[3,6]] [1,1,1,0,0,0]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[[1,4],[2,5],[3,6]] [1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>[[1,5],[2,6],[3,7],[4,8]] [1,0,1,0,1,1,0,0]=>[[1,3,5,6],[2,4,7,8]]=>[2,4,7,8,1,3,5,6]=>[6,5,3,1,8,7,4,2]=>[[1,5],[2,6],[3,7],[4,8]] [1,0,1,1,0,0,1,0]=>[[1,3,4,7],[2,5,6,8]]=>[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>[[1,5],[2,6],[3,7],[4,8]] [1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]]=>[3,4,6,8,1,2,5,7]=>[7,5,2,1,8,6,4,3]=>[[1,5],[2,6],[3,7],[4,8]] [1,1,0,0,1,1,0,0]=>[[1,2,5,6],[3,4,7,8]]=>[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]=>[[1,5],[2,6],[3,7],[4,8]] [1,1,0,1,0,0,1,0]=>[[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[7,4,2,1,8,6,5,3]=>[[1,5],[2,6],[3,7],[4,8]] [1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>[[1,5],[2,6],[3,7],[4,8]] [1,1,0,1,1,0,0,0]=>[[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[5,4,2,1,8,7,6,3]=>[[1,5],[2,6],[3,7],[4,8]] [1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[7,3,2,1,8,6,5,4]=>[[1,5],[2,6],[3,7],[4,8]] [1,1,1,1,0,0,0,0]=>[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8]]
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
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.