Identifier
Mp00042:
Integer partitions
—initial tableau⟶
Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1
[1]=>[[1]]=>[1]=>[1]
[2]=>[[1,2]]=>[2]=>[1,1]
[1,1]=>[[1],[2]]=>[1,1]=>[2]
[3]=>[[1,2,3]]=>[3]=>[1,1,1]
[2,1]=>[[1,2],[3]]=>[2,1]=>[2,1]
[1,1,1]=>[[1],[2],[3]]=>[1,1,1]=>[3]
[4]=>[[1,2,3,4]]=>[4]=>[1,1,1,1]
[3,1]=>[[1,2,3],[4]]=>[3,1]=>[2,1,1]
[2,2]=>[[1,2],[3,4]]=>[2,2]=>[1,2,1]
[2,1,1]=>[[1,2],[3],[4]]=>[2,1,1]=>[3,1]
[1,1,1,1]=>[[1],[2],[3],[4]]=>[1,1,1,1]=>[4]
[5]=>[[1,2,3,4,5]]=>[5]=>[1,1,1,1,1]
[4,1]=>[[1,2,3,4],[5]]=>[4,1]=>[2,1,1,1]
[3,2]=>[[1,2,3],[4,5]]=>[3,2]=>[1,2,1,1]
[3,1,1]=>[[1,2,3],[4],[5]]=>[3,1,1]=>[3,1,1]
[2,2,1]=>[[1,2],[3,4],[5]]=>[2,2,1]=>[2,2,1]
[2,1,1,1]=>[[1,2],[3],[4],[5]]=>[2,1,1,1]=>[4,1]
[1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[1,1,1,1,1]=>[5]
[6]=>[[1,2,3,4,5,6]]=>[6]=>[1,1,1,1,1,1]
[5,1]=>[[1,2,3,4,5],[6]]=>[5,1]=>[2,1,1,1,1]
[4,2]=>[[1,2,3,4],[5,6]]=>[4,2]=>[1,2,1,1,1]
[4,1,1]=>[[1,2,3,4],[5],[6]]=>[4,1,1]=>[3,1,1,1]
[3,3]=>[[1,2,3],[4,5,6]]=>[3,3]=>[1,1,2,1,1]
[3,2,1]=>[[1,2,3],[4,5],[6]]=>[3,2,1]=>[2,2,1,1]
[3,1,1,1]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]=>[4,1,1]
[2,2,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]=>[1,2,2,1]
[2,2,1,1]=>[[1,2],[3,4],[5],[6]]=>[2,2,1,1]=>[3,2,1]
[2,1,1,1,1]=>[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]=>[5,1]
[1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,1]=>[6]
[7]=>[[1,2,3,4,5,6,7]]=>[7]=>[1,1,1,1,1,1,1]
[6,1]=>[[1,2,3,4,5,6],[7]]=>[6,1]=>[2,1,1,1,1,1]
[5,2]=>[[1,2,3,4,5],[6,7]]=>[5,2]=>[1,2,1,1,1,1]
[5,1,1]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]=>[3,1,1,1,1]
[4,3]=>[[1,2,3,4],[5,6,7]]=>[4,3]=>[1,1,2,1,1,1]
[4,2,1]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]=>[2,2,1,1,1]
[4,1,1,1]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]=>[4,1,1,1]
[3,3,1]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]=>[2,1,2,1,1]
[3,2,2]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]=>[1,2,2,1,1]
[3,2,1,1]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]=>[3,2,1,1]
[3,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]=>[5,1,1]
[2,2,2,1]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]=>[2,2,2,1]
[2,2,1,1,1]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,1,1,1]=>[4,2,1]
[2,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,1]=>[6,1]
[1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,1]=>[7]
[8]=>[[1,2,3,4,5,6,7,8]]=>[8]=>[1,1,1,1,1,1,1,1]
[7,1]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]=>[2,1,1,1,1,1,1]
[6,2]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]=>[1,2,1,1,1,1,1]
[6,1,1]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]=>[3,1,1,1,1,1]
[5,3]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]=>[1,1,2,1,1,1,1]
[5,2,1]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]=>[2,2,1,1,1,1]
[5,1,1,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]=>[4,1,1,1,1]
[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]=>[1,1,1,2,1,1,1]
[4,3,1]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]=>[2,1,2,1,1,1]
[4,2,2]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]=>[1,2,2,1,1,1]
[4,2,1,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]=>[3,2,1,1,1]
[4,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]=>[5,1,1,1]
[3,3,2]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]=>[1,2,1,2,1,1]
[3,3,1,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,1,1]=>[3,1,2,1,1]
[3,2,2,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]=>[2,2,2,1,1]
[3,2,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,1,1,1]=>[4,2,1,1]
[3,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]=>[6,1,1]
[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]=>[1,2,2,2,1]
[2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,1,1]=>[3,2,2,1]
[2,2,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,1,1,1,1]=>[5,2,1]
[2,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]=>[7,1]
[1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,1]=>[8]
[9]=>[[1,2,3,4,5,6,7,8,9]]=>[9]=>[1,1,1,1,1,1,1,1,1]
[8,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]=>[2,1,1,1,1,1,1,1]
[7,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]=>[1,2,1,1,1,1,1,1]
[7,1,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,1,1]=>[3,1,1,1,1,1,1]
[6,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]=>[1,1,2,1,1,1,1,1]
[6,2,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[6,2,1]=>[2,2,1,1,1,1,1]
[6,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,1,1,1]=>[4,1,1,1,1,1]
[5,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]=>[1,1,1,2,1,1,1,1]
[5,3,1]=>[[1,2,3,4,5],[6,7,8],[9]]=>[5,3,1]=>[2,1,2,1,1,1,1]
[5,2,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[5,2,2]=>[1,2,2,1,1,1,1]
[5,2,1,1]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[5,2,1,1]=>[3,2,1,1,1,1]
[5,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,1,1,1,1]=>[5,1,1,1,1]
[4,4,1]=>[[1,2,3,4],[5,6,7,8],[9]]=>[4,4,1]=>[2,1,1,2,1,1,1]
[4,3,2]=>[[1,2,3,4],[5,6,7],[8,9]]=>[4,3,2]=>[1,2,1,2,1,1,1]
[4,3,1,1]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[4,3,1,1]=>[3,1,2,1,1,1]
[4,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[4,2,2,1]=>[2,2,2,1,1,1]
[4,2,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[4,2,1,1,1]=>[4,2,1,1,1]
[4,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[4,1,1,1,1,1]=>[6,1,1,1]
[3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[3,3,3]=>[1,1,2,1,2,1,1]
[3,3,2,1]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[3,3,2,1]=>[2,2,1,2,1,1]
[3,3,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[3,3,1,1,1]=>[4,1,2,1,1]
[3,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9]]=>[3,2,2,2]=>[1,2,2,2,1,1]
[3,2,2,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9]]=>[3,2,2,1,1]=>[3,2,2,1,1]
[3,2,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[3,2,1,1,1,1]=>[5,2,1,1]
[3,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,1,1,1,1,1,1]=>[7,1,1]
[2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[2,2,2,2,1]=>[2,2,2,2,1]
[2,2,2,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9]]=>[2,2,2,1,1,1]=>[4,2,2,1]
[2,2,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[2,2,1,1,1,1,1]=>[6,2,1]
[2,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,1,1,1,1,1,1,1]=>[8,1]
[1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,1]=>[9]
[10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[10]=>[1,1,1,1,1,1,1,1,1,1]
[9,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]=>[2,1,1,1,1,1,1,1,1]
[8,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]=>[1,2,1,1,1,1,1,1,1]
[8,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,1,1]=>[3,1,1,1,1,1,1,1]
[7,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]=>[1,1,2,1,1,1,1,1,1]
[7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[7,2,1]=>[2,2,1,1,1,1,1,1]
[7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,1,1,1]=>[4,1,1,1,1,1,1]
[6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]=>[1,1,1,2,1,1,1,1,1]
[6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[6,3,1]=>[2,1,2,1,1,1,1,1]
[6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[6,2,2]=>[1,2,2,1,1,1,1,1]
[6,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[6,2,1,1]=>[3,2,1,1,1,1,1]
[6,1,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,1,1,1,1]=>[5,1,1,1,1,1]
[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]=>[1,1,1,1,2,1,1,1,1]
[5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[5,4,1]=>[2,1,1,2,1,1,1,1]
[5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[5,3,2]=>[1,2,1,2,1,1,1,1]
[5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[5,3,1,1]=>[3,1,2,1,1,1,1]
[5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[5,2,2,1]=>[2,2,2,1,1,1,1]
[5,2,1,1,1]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[5,2,1,1,1]=>[4,2,1,1,1,1]
[5,1,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,1,1,1,1,1]=>[6,1,1,1,1]
[4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[4,4,2]=>[1,2,1,1,2,1,1,1]
[4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[4,4,1,1]=>[3,1,1,2,1,1,1]
[4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[4,3,3]=>[1,1,2,1,2,1,1,1]
[4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[4,3,2,1]=>[2,2,1,2,1,1,1]
[4,3,1,1,1]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[4,3,1,1,1]=>[4,1,2,1,1,1]
[4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[4,2,2,2]=>[1,2,2,2,1,1,1]
[4,2,2,1,1]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[4,2,2,1,1]=>[3,2,2,1,1,1]
[4,2,1,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[4,2,1,1,1,1]=>[5,2,1,1,1]
[4,1,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[4,1,1,1,1,1,1]=>[7,1,1,1]
[3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[3,3,3,1]=>[2,1,2,1,2,1,1]
[3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[3,3,2,2]=>[1,2,2,1,2,1,1]
[3,3,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[3,3,2,1,1]=>[3,2,1,2,1,1]
[3,3,1,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[3,3,1,1,1,1]=>[5,1,2,1,1]
[3,2,2,2,1]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[3,2,2,2,1]=>[2,2,2,2,1,1]
[3,2,2,1,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[3,2,2,1,1,1]=>[4,2,2,1,1]
[3,2,1,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[3,2,1,1,1,1,1]=>[6,2,1,1]
[3,1,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[3,1,1,1,1,1,1,1]=>[8,1,1]
[2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[2,2,2,2,2]=>[1,2,2,2,2,1]
[2,2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[2,2,2,2,1,1]=>[3,2,2,2,1]
[2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[2,2,2,1,1,1,1]=>[5,2,2,1]
[2,2,1,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[2,2,1,1,1,1,1,1]=>[7,2,1]
[2,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,1,1,1,1,1,1,1,1]=>[9,1]
[1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[1,1,1,1,1,1,1,1,1,1]=>[10]
[5,4,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11]]=>[5,4,2]=>[1,2,1,1,2,1,1,1,1]
[5,4,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10],[11]]=>[5,4,1,1]=>[3,1,1,2,1,1,1,1]
[5,3,3]=>[[1,2,3,4,5],[6,7,8],[9,10,11]]=>[5,3,3]=>[1,1,2,1,2,1,1,1,1]
[5,3,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11]]=>[5,3,2,1]=>[2,2,1,2,1,1,1,1]
[5,3,1,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10],[11]]=>[5,3,1,1,1]=>[4,1,2,1,1,1,1]
[5,2,2,2]=>[[1,2,3,4,5],[6,7],[8,9],[10,11]]=>[5,2,2,2]=>[1,2,2,2,1,1,1,1]
[5,2,2,1,1]=>[[1,2,3,4,5],[6,7],[8,9],[10],[11]]=>[5,2,2,1,1]=>[3,2,2,1,1,1,1]
[4,4,3]=>[[1,2,3,4],[5,6,7,8],[9,10,11]]=>[4,4,3]=>[1,1,2,1,1,2,1,1,1]
[4,4,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11]]=>[4,4,2,1]=>[2,2,1,1,2,1,1,1]
[4,4,1,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10],[11]]=>[4,4,1,1,1]=>[4,1,1,2,1,1,1]
[4,3,3,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11]]=>[4,3,3,1]=>[2,1,2,1,2,1,1,1]
[4,3,2,2]=>[[1,2,3,4],[5,6,7],[8,9],[10,11]]=>[4,3,2,2]=>[1,2,2,1,2,1,1,1]
[4,3,2,1,1]=>[[1,2,3,4],[5,6,7],[8,9],[10],[11]]=>[4,3,2,1,1]=>[3,2,1,2,1,1,1]
[4,2,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11]]=>[4,2,2,2,1]=>[2,2,2,2,1,1,1]
[3,3,3,2]=>[[1,2,3],[4,5,6],[7,8,9],[10,11]]=>[3,3,3,2]=>[1,2,1,2,1,2,1,1]
[3,3,3,1,1]=>[[1,2,3],[4,5,6],[7,8,9],[10],[11]]=>[3,3,3,1,1]=>[3,1,2,1,2,1,1]
[3,3,2,2,1]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11]]=>[3,3,2,2,1]=>[2,2,2,1,2,1,1]
[12]=>[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]
[6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]=>[1,1,1,1,1,2,1,1,1,1,1]
[6,4,2]=>[[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[6,4,2]=>[1,2,1,1,2,1,1,1,1,1]
[5,4,3]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12]]=>[5,4,3]=>[1,1,2,1,1,2,1,1,1,1]
[5,4,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12]]=>[5,4,2,1]=>[2,2,1,1,2,1,1,1,1]
[5,4,1,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10],[11],[12]]=>[5,4,1,1,1]=>[4,1,1,2,1,1,1,1]
[5,3,3,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12]]=>[5,3,3,1]=>[2,1,2,1,2,1,1,1,1]
[5,3,2,2]=>[[1,2,3,4,5],[6,7,8],[9,10],[11,12]]=>[5,3,2,2]=>[1,2,2,1,2,1,1,1,1]
[5,3,2,1,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11],[12]]=>[5,3,2,1,1]=>[3,2,1,2,1,1,1,1]
[5,2,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10,11],[12]]=>[5,2,2,2,1]=>[2,2,2,2,1,1,1,1]
[4,4,3,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12]]=>[4,4,3,1]=>[2,1,2,1,1,2,1,1,1]
[4,4,2,2]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[4,4,2,2]=>[1,2,2,1,1,2,1,1,1]
[4,4,2,1,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11],[12]]=>[4,4,2,1,1]=>[3,2,1,1,2,1,1,1]
[4,3,3,2]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12]]=>[4,3,3,2]=>[1,2,1,2,1,2,1,1,1]
[4,3,3,1,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11],[12]]=>[4,3,3,1,1]=>[3,1,2,1,2,1,1,1]
[4,3,2,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10,11],[12]]=>[4,3,2,2,1]=>[2,2,2,1,2,1,1,1]
[4,2,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[4,2,2,2,2]=>[1,2,2,2,2,1,1,1]
[3,3,3,2,1]=>[[1,2,3],[4,5,6],[7,8,9],[10,11],[12]]=>[3,3,3,2,1]=>[2,2,1,2,1,2,1,1]
[3,3,2,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]]=>[3,3,2,2,1,1]=>[3,2,2,1,2,1,1]
[2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[2,2,2,2,2,2]=>[1,2,2,2,2,2,1]
[1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[12]
[5,4,3,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]]=>[5,4,3,1]=>[2,1,2,1,1,2,1,1,1,1]
[5,4,2,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]]=>[5,4,2,2]=>[1,2,2,1,1,2,1,1,1,1]
[5,4,2,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]]=>[5,4,2,1,1]=>[3,2,1,1,2,1,1,1,1]
[5,3,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]]=>[5,3,3,2]=>[1,2,1,2,1,2,1,1,1,1]
[5,3,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]]=>[5,3,3,1,1]=>[3,1,2,1,2,1,1,1,1]
[5,3,2,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]=>[5,3,2,2,1]=>[2,2,2,1,2,1,1,1,1]
[4,4,3,2]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]]=>[4,4,3,2]=>[1,2,1,2,1,1,2,1,1,1]
[4,4,3,1,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]]=>[4,4,3,1,1]=>[3,1,2,1,1,2,1,1,1]
[4,4,2,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]]=>[4,4,2,2,1]=>[2,2,2,1,1,2,1,1,1]
[4,3,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]]=>[4,3,3,2,1]=>[2,2,1,2,1,2,1,1,1]
[7,7]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]]=>[7,7]=>[1,1,1,1,1,1,2,1,1,1,1,1,1]
[5,4,3,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]]=>[5,4,3,2]=>[1,2,1,2,1,1,2,1,1,1,1]
[5,4,3,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]]=>[5,4,3,1,1]=>[3,1,2,1,1,2,1,1,1,1]
[5,4,2,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]]=>[5,4,2,2,1]=>[2,2,2,1,1,2,1,1,1,1]
[5,3,3,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]]=>[5,3,3,2,1]=>[2,2,1,2,1,2,1,1,1,1]
[4,4,3,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]]=>[4,4,3,2,1]=>[2,2,1,2,1,1,2,1,1,1]
[2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]]=>[2,2,2,2,2,2,2]=>[1,2,2,2,2,2,2,1]
[5,4,3,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]]=>[5,4,3,2,1]=>[2,2,1,2,1,1,2,1,1,1,1]
[2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16]]=>[2,2,2,2,2,2,2,2]=>[1,2,2,2,2,2,2,2,1]
[2,2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18]]=>[2,2,2,2,2,2,2,2,2]=>[1,2,2,2,2,2,2,2,2,1]
[2,2,2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18],[19,20]]=>[2,2,2,2,2,2,2,2,2,2]=>[1,2,2,2,2,2,2,2,2,2,1]
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
Map
conjugate
searching the database
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