Identifier
Mp00045:
Integer partitions
—reading tableau⟶
Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1
[1]=>[[1]]=>[1]=>[1]
[2]=>[[1,2]]=>[1,2]=>[2]
[1,1]=>[[1],[2]]=>[2,1]=>[1,1]
[3]=>[[1,2,3]]=>[1,2,3]=>[3]
[2,1]=>[[1,3],[2]]=>[2,1,3]=>[1,2]
[1,1,1]=>[[1],[2],[3]]=>[3,2,1]=>[1,1,1]
[4]=>[[1,2,3,4]]=>[1,2,3,4]=>[4]
[3,1]=>[[1,3,4],[2]]=>[2,1,3,4]=>[1,3]
[2,2]=>[[1,2],[3,4]]=>[3,4,1,2]=>[2,2]
[2,1,1]=>[[1,4],[2],[3]]=>[3,2,1,4]=>[1,1,2]
[1,1,1,1]=>[[1],[2],[3],[4]]=>[4,3,2,1]=>[1,1,1,1]
[5]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[5]
[4,1]=>[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[1,4]
[3,2]=>[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[2,3]
[3,1,1]=>[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[1,1,3]
[2,2,1]=>[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[1,2,2]
[2,1,1,1]=>[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[1,1,1,2]
[1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[1,1,1,1,1]
[6]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[6]
[5,1]=>[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[1,5]
[4,2]=>[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[2,4]
[4,1,1]=>[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[1,1,4]
[3,3]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[3,3]
[3,2,1]=>[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[1,2,3]
[3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[1,1,1,3]
[2,2,2]=>[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,2,2]
[2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[1,1,2,2]
[2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[7]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[7]
[6,1]=>[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[1,6]
[5,2]=>[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[2,5]
[5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[1,1,5]
[4,3]=>[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[3,4]
[4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[1,2,4]
[4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[1,3,3]
[3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[2,2,3]
[3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[1,1,2,3]
[3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[1,2,2,2]
[2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[1,1,1,2,2]
[2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[8]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[8]
[7,1]=>[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[1,7]
[6,2]=>[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[2,6]
[6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[5,3]=>[[1,2,3,7,8],[4,5,6]]=>[4,5,6,1,2,3,7,8]=>[3,5]
[5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[1,2,5]
[5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[4,4]
[4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[1,3,4]
[4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[2,2,4]
[4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[1,1,2,4]
[4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5]=>[2,3,3]
[3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[1,1,3,3]
[3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[1,2,2,3]
[3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[1,1,1,2,3]
[3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[1,1,2,2,2]
[2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[1,1,1,1,2,2]
[2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
[9]=>[[1,2,3,4,5,6,7,8,9]]=>[1,2,3,4,5,6,7,8,9]=>[9]
[8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[1,8]
[7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[3,4,1,2,5,6,7,8,9]=>[2,7]
[7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[1,1,7]
[6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[4,5,6,1,2,3,7,8,9]=>[3,6]
[6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9]=>[1,2,6]
[6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9]=>[1,1,1,6]
[5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9]=>[4,5]
[5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9]=>[1,3,5]
[5,2,2]=>[[1,2,7,8,9],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9]=>[2,2,5]
[5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9]=>[1,1,2,5]
[5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9]=>[1,1,1,1,5]
[4,4,1]=>[[1,3,4,5],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5]=>[1,4,4]
[4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9]=>[2,3,4]
[4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9]=>[1,1,3,4]
[4,2,2,1]=>[[1,3,8,9],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9]=>[1,2,2,4]
[4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9]=>[1,1,1,2,4]
[4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[1,1,1,1,1,4]
[3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[3,3,3]
[3,3,2,1]=>[[1,3,6],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6]=>[1,2,3,3]
[3,3,1,1,1]=>[[1,5,6],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6]=>[1,1,1,3,3]
[3,2,2,2]=>[[1,2,9],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9]=>[2,2,2,3]
[3,2,2,1,1]=>[[1,4,9],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9]=>[1,1,2,2,3]
[3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9]=>[1,1,1,1,2,3]
[3,1,1,1,1,1,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,3]
[2,2,2,2,1]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3]=>[1,2,2,2,2]
[2,2,2,1,1,1]=>[[1,5],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5]=>[1,1,1,2,2,2]
[2,2,1,1,1,1,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7]=>[1,1,1,1,1,2,2]
[2,1,1,1,1,1,1,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1]
[10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[1,2,3,4,5,6,7,8,9,10]=>[10]
[9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[1,9]
[8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[3,4,1,2,5,6,7,8,9,10]=>[2,8]
[8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[1,1,8]
[7,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[4,5,6,1,2,3,7,8,9,10]=>[3,7]
[7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9,10]=>[1,2,7]
[7,1,1,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9,10]=>[1,1,1,7]
[6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9,10]=>[4,6]
[6,3,1]=>[[1,3,4,8,9,10],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9,10]=>[1,3,6]
[6,2,2]=>[[1,2,7,8,9,10],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9,10]=>[2,2,6]
[6,2,1,1]=>[[1,4,7,8,9,10],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9,10]=>[1,1,2,6]
[6,1,1,1,1]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>[1,1,1,1,6]
[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[5,5]
[5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5,10]=>[1,4,5]
[5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9,10]=>[2,3,5]
[5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9,10]=>[1,1,3,5]
[5,2,2,1]=>[[1,3,8,9,10],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9,10]=>[1,2,2,5]
[5,2,1,1,1]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9,10]=>[1,1,1,2,5]
[5,1,1,1,1,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9,10]=>[1,1,1,1,1,5]
[4,4,2]=>[[1,2,5,6],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6]=>[2,4,4]
[4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[7,3,2,8,9,10,1,4,5,6]=>[1,1,4,4]
[4,3,3]=>[[1,2,3,10],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3,10]=>[3,3,4]
[4,3,2,1]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6,10]=>[1,2,3,4]
[4,3,1,1,1]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6,10]=>[1,1,1,3,4]
[4,2,2,2]=>[[1,2,9,10],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9,10]=>[2,2,2,4]
[4,2,2,1,1]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9,10]=>[1,1,2,2,4]
[4,2,1,1,1,1]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9,10]=>[1,1,1,1,2,4]
[4,1,1,1,1,1,1]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9,10]=>[1,1,1,1,1,1,4]
[3,3,3,1]=>[[1,3,4],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4]=>[1,3,3,3]
[3,3,2,2]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>[8,9,5,6,3,4,10,1,2,7]=>[2,2,3,3]
[3,3,2,1,1]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[8,5,3,9,2,6,10,1,4,7]=>[1,1,2,3,3]
[3,3,1,1,1,1]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[8,5,4,3,2,9,10,1,6,7]=>[1,1,1,1,3,3]
[3,2,2,2,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10]=>[1,2,2,2,3]
[3,2,2,1,1,1]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5,10]=>[1,1,1,2,2,3]
[3,2,1,1,1,1,1]=>[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7,10]=>[1,1,1,1,1,2,3]
[3,1,1,1,1,1,1,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9,10]=>[1,1,1,1,1,1,1,3]
[2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2]
[2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[9,7,5,10,3,8,2,6,1,4]=>[1,1,2,2,2,2]
[2,2,2,1,1,1,1]=>[[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>[9,7,5,4,3,10,2,8,1,6]=>[1,1,1,1,2,2,2]
[2,2,1,1,1,1,1,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,10,1,8]=>[1,1,1,1,1,1,2,2]
[2,1,1,1,1,1,1,1,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]
[5,4,2]=>[[1,2,5,6,11],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6,11]=>[2,4,5]
[5,4,1,1]=>[[1,4,5,6,11],[2,8,9,10],[3],[7]]=>[7,3,2,8,9,10,1,4,5,6,11]=>[1,1,4,5]
[5,3,3]=>[[1,2,3,10,11],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3,10,11]=>[3,3,5]
[5,3,2,1]=>[[1,3,6,10,11],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6,10,11]=>[1,2,3,5]
[5,3,1,1,1]=>[[1,5,6,10,11],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6,10,11]=>[1,1,1,3,5]
[5,2,2,2]=>[[1,2,9,10,11],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9,10,11]=>[2,2,2,5]
[5,2,2,1,1]=>[[1,4,9,10,11],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9,10,11]=>[1,1,2,2,5]
[4,4,3]=>[[1,2,3,7],[4,5,6,11],[8,9,10]]=>[8,9,10,4,5,6,11,1,2,3,7]=>[3,4,4]
[4,4,2,1]=>[[1,3,6,7],[2,5,10,11],[4,9],[8]]=>[8,4,9,2,5,10,11,1,3,6,7]=>[1,2,4,4]
[4,4,1,1,1]=>[[1,5,6,7],[2,9,10,11],[3],[4],[8]]=>[8,4,3,2,9,10,11,1,5,6,7]=>[1,1,1,4,4]
[4,3,3,1]=>[[1,3,4,11],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4,11]=>[1,3,3,4]
[4,3,2,2]=>[[1,2,7,11],[3,4,10],[5,6],[8,9]]=>[8,9,5,6,3,4,10,1,2,7,11]=>[2,2,3,4]
[4,3,2,1,1]=>[[1,4,7,11],[2,6,10],[3,9],[5],[8]]=>[8,5,3,9,2,6,10,1,4,7,11]=>[1,1,2,3,4]
[4,2,2,2,1]=>[[1,3,10,11],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10,11]=>[1,2,2,2,4]
[3,3,3,2]=>[[1,2,5],[3,4,8],[6,7,11],[9,10]]=>[9,10,6,7,11,3,4,8,1,2,5]=>[2,3,3,3]
[3,3,3,1,1]=>[[1,4,5],[2,7,8],[3,10,11],[6],[9]]=>[9,6,3,10,11,2,7,8,1,4,5]=>[1,1,3,3,3]
[3,3,2,2,1]=>[[1,3,8],[2,5,11],[4,7],[6,10],[9]]=>[9,6,10,4,7,2,5,11,1,3,8]=>[1,2,2,3,3]
[12]=>[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12]
[6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[6,6]
[6,4,2]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6,11,12]=>[2,4,6]
[5,4,3]=>[[1,2,3,7,12],[4,5,6,11],[8,9,10]]=>[8,9,10,4,5,6,11,1,2,3,7,12]=>[3,4,5]
[5,4,2,1]=>[[1,3,6,7,12],[2,5,10,11],[4,9],[8]]=>[8,4,9,2,5,10,11,1,3,6,7,12]=>[1,2,4,5]
[5,4,1,1,1]=>[[1,5,6,7,12],[2,9,10,11],[3],[4],[8]]=>[8,4,3,2,9,10,11,1,5,6,7,12]=>[1,1,1,4,5]
[5,3,3,1]=>[[1,3,4,11,12],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4,11,12]=>[1,3,3,5]
[5,3,2,2]=>[[1,2,7,11,12],[3,4,10],[5,6],[8,9]]=>[8,9,5,6,3,4,10,1,2,7,11,12]=>[2,2,3,5]
[5,3,2,1,1]=>[[1,4,7,11,12],[2,6,10],[3,9],[5],[8]]=>[8,5,3,9,2,6,10,1,4,7,11,12]=>[1,1,2,3,5]
[5,2,2,2,1]=>[[1,3,10,11,12],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10,11,12]=>[1,2,2,2,5]
[4,4,3,1]=>[[1,3,4,8],[2,6,7,12],[5,10,11],[9]]=>[9,5,10,11,2,6,7,12,1,3,4,8]=>[1,3,4,4]
[4,4,2,2]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>[9,10,5,6,3,4,11,12,1,2,7,8]=>[2,2,4,4]
[4,4,2,1,1]=>[[1,4,7,8],[2,6,11,12],[3,10],[5],[9]]=>[9,5,3,10,2,6,11,12,1,4,7,8]=>[1,1,2,4,4]
[4,3,3,2]=>[[1,2,5,12],[3,4,8],[6,7,11],[9,10]]=>[9,10,6,7,11,3,4,8,1,2,5,12]=>[2,3,3,4]
[4,3,3,1,1]=>[[1,4,5,12],[2,7,8],[3,10,11],[6],[9]]=>[9,6,3,10,11,2,7,8,1,4,5,12]=>[1,1,3,3,4]
[4,3,2,2,1]=>[[1,3,8,12],[2,5,11],[4,7],[6,10],[9]]=>[9,6,10,4,7,2,5,11,1,3,8,12]=>[1,2,2,3,4]
[3,3,3,2,1]=>[[1,3,6],[2,5,9],[4,8,12],[7,11],[10]]=>[10,7,11,4,8,12,2,5,9,1,3,6]=>[1,2,3,3,3]
[3,3,2,2,1,1]=>[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>[10,7,5,11,3,8,2,6,12,1,4,9]=>[1,1,2,2,3,3]
[2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2,2]
[1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]
[5,4,3,1]=>[[1,3,4,8,13],[2,6,7,12],[5,10,11],[9]]=>[9,5,10,11,2,6,7,12,1,3,4,8,13]=>[1,3,4,5]
[5,4,2,2]=>[[1,2,7,8,13],[3,4,11,12],[5,6],[9,10]]=>[9,10,5,6,3,4,11,12,1,2,7,8,13]=>[2,2,4,5]
[5,4,2,1,1]=>[[1,4,7,8,13],[2,6,11,12],[3,10],[5],[9]]=>[9,5,3,10,2,6,11,12,1,4,7,8,13]=>[1,1,2,4,5]
[5,3,3,2]=>[[1,2,5,12,13],[3,4,8],[6,7,11],[9,10]]=>[9,10,6,7,11,3,4,8,1,2,5,12,13]=>[2,3,3,5]
[5,3,3,1,1]=>[[1,4,5,12,13],[2,7,8],[3,10,11],[6],[9]]=>[9,6,3,10,11,2,7,8,1,4,5,12,13]=>[1,1,3,3,5]
[5,3,2,2,1]=>[[1,3,8,12,13],[2,5,11],[4,7],[6,10],[9]]=>[9,6,10,4,7,2,5,11,1,3,8,12,13]=>[1,2,2,3,5]
[4,4,3,2]=>[[1,2,5,9],[3,4,8,13],[6,7,12],[10,11]]=>[10,11,6,7,12,3,4,8,13,1,2,5,9]=>[2,3,4,4]
[4,4,3,1,1]=>[[1,4,5,9],[2,7,8,13],[3,11,12],[6],[10]]=>[10,6,3,11,12,2,7,8,13,1,4,5,9]=>[1,1,3,4,4]
[4,4,2,2,1]=>[[1,3,8,9],[2,5,12,13],[4,7],[6,11],[10]]=>[10,6,11,4,7,2,5,12,13,1,3,8,9]=>[1,2,2,4,4]
[4,3,3,2,1]=>[[1,3,6,13],[2,5,9],[4,8,12],[7,11],[10]]=>[10,7,11,4,8,12,2,5,9,1,3,6,13]=>[1,2,3,3,4]
[5,4,3,2]=>[[1,2,5,9,14],[3,4,8,13],[6,7,12],[10,11]]=>[10,11,6,7,12,3,4,8,13,1,2,5,9,14]=>[2,3,4,5]
[5,4,3,1,1]=>[[1,4,5,9,14],[2,7,8,13],[3,11,12],[6],[10]]=>[10,6,3,11,12,2,7,8,13,1,4,5,9,14]=>[1,1,3,4,5]
[5,4,2,2,1]=>[[1,3,8,9,14],[2,5,12,13],[4,7],[6,11],[10]]=>[10,6,11,4,7,2,5,12,13,1,3,8,9,14]=>[1,2,2,4,5]
[5,3,3,2,1]=>[[1,3,6,13,14],[2,5,9],[4,8,12],[7,11],[10]]=>[10,7,11,4,8,12,2,5,9,1,3,6,13,14]=>[1,2,3,3,5]
[4,4,3,2,1]=>[[1,3,6,10],[2,5,9,14],[4,8,13],[7,12],[11]]=>[11,7,12,4,8,13,2,5,9,14,1,3,6,10]=>[1,2,3,4,4]
[5,4,3,2,1]=>[[1,3,6,10,15],[2,5,9,14],[4,8,13],[7,12],[11]]=>[11,7,12,4,8,13,2,5,9,14,1,3,6,10,15]=>[1,2,3,4,5]
[]=>[]=>[]=>[]
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.
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
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
searching the database
Sorry, this map was not found in the database.