Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1Cc0007;cc-rep-4
[1]=>[[1]]=>[1]=>[1]=>[[1]] [2]=>[[1,2]]=>[1,2]=>[2,1]=>[[1],[2]] [1,1]=>[[1],[2]]=>[2,1]=>[1,2]=>[[1,2]] [3]=>[[1,2,3]]=>[1,2,3]=>[3,2,1]=>[[1],[2],[3]] [2,1]=>[[1,2],[3]]=>[3,1,2]=>[2,1,3]=>[[1,3],[2]] [1,1,1]=>[[1],[2],[3]]=>[3,2,1]=>[1,2,3]=>[[1,2,3]] [4]=>[[1,2,3,4]]=>[1,2,3,4]=>[4,3,2,1]=>[[1],[2],[3],[4]] [3,1]=>[[1,2,3],[4]]=>[4,1,2,3]=>[3,2,1,4]=>[[1,4],[2],[3]] [2,2]=>[[1,2],[3,4]]=>[3,4,1,2]=>[2,1,4,3]=>[[1,3],[2,4]] [2,1,1]=>[[1,2],[3],[4]]=>[4,3,1,2]=>[2,1,3,4]=>[[1,3,4],[2]] [1,1,1,1]=>[[1],[2],[3],[4]]=>[4,3,2,1]=>[1,2,3,4]=>[[1,2,3,4]] [5]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]] [4,1]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[[1,5],[2],[3],[4]] [3,2]=>[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[[1,4],[2,5],[3]] [3,1,1]=>[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]] [2,2,1]=>[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[[1,3,5],[2,4]] [2,1,1,1]=>[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[[1,3,4,5],[2]] [1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[[1,2,3,4,5]] [6]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]] [5,1]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]] [4,2]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[[1,5],[2,6],[3],[4]] [4,1,1]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]] [3,3]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[[1,4],[2,5],[3,6]] [3,2,1]=>[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[[1,4,6],[2,5],[3]] [3,1,1,1]=>[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]] [2,2,2]=>[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]] [2,2,1,1]=>[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[[1,3,5,6],[2,4]] [2,1,1,1,1]=>[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]] [1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]] [7]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7]] [6,1]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]] [5,2]=>[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[[1,6],[2,7],[3],[4],[5]] [5,1,1]=>[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]] [4,3]=>[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[[1,5],[2,6],[3,7],[4]] [4,2,1]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[[1,5,7],[2,6],[3],[4]] [4,1,1,1]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]] [3,3,1]=>[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[[1,4,7],[2,5],[3,6]] [3,2,2]=>[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3]] [3,2,1,1]=>[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3]] [3,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]] [2,2,2,1]=>[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6]] [2,2,1,1,1]=>[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[[1,3,5,6,7],[2,4]] [2,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]] [1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]] [8]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]] [7,1]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7]] [6,2]=>[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[[1,7],[2,8],[3],[4],[5],[6]] [6,1,1]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>[[1,7,8],[2],[3],[4],[5],[6]] [5,3]=>[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>[[1,6],[2,7],[3,8],[4],[5]] [5,2,1]=>[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>[[1,6,8],[2,7],[3],[4],[5]] [5,1,1,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>[[1,6,7,8],[2],[3],[4],[5]] [4,4]=>[[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]] [4,3,1]=>[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>[[1,5,8],[2,6],[3,7],[4]] [4,2,2]=>[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[[1,5,7],[2,6,8],[3],[4]] [4,2,1,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>[[1,5,7,8],[2,6],[3],[4]] [4,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]] [3,3,2]=>[[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>[[1,4,7],[2,5,8],[3,6]] [3,3,1,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>[[1,4,7,8],[2,5],[3,6]] [3,2,2,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>[[1,4,6,8],[2,5,7],[3]] [3,2,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>[[1,4,6,7,8],[2,5],[3]] [3,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]] [2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]] [2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]] [2,2,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]] [2,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[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]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]] [9]=>[[1,2,3,4,5,6,7,8,9]]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]] [8,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]] [7,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8]=>[[1,8],[2,9],[3],[4],[5],[6],[7]] [7,1,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]] [6,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7]=>[[1,7],[2,8],[3,9],[4],[5],[6]] [6,2,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[9,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,9]=>[[1,7,9],[2,8],[3],[4],[5],[6]] [6,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [5,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5]] [5,3,1]=>[[1,2,3,4,5],[6,7,8],[9]]=>[9,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,9]=>[[1,6,9],[2,7],[3,8],[4],[5]] [5,2,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[8,9,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,9,8]=>[[1,6,8],[2,7,9],[3],[4],[5]] [5,2,1,1]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[9,8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8,9]=>[[1,6,8,9],[2,7],[3],[4],[5]] [5,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]] [4,4,1]=>[[1,2,3,4],[5,6,7,8],[9]]=>[9,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,9]=>[[1,5,9],[2,6],[3,7],[4,8]] [4,3,2]=>[[1,2,3,4],[5,6,7],[8,9]]=>[8,9,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,9,8]=>[[1,5,8],[2,6,9],[3,7],[4]] [4,3,1,1]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[9,8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8,9]=>[[1,5,8,9],[2,6],[3,7],[4]] [4,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,9]=>[[1,5,7,9],[2,6,8],[3],[4]] [4,2,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8,9]=>[[1,5,7,8,9],[2,6],[3],[4]] [4,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]] [3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7]=>[[1,4,7],[2,5,8],[3,6,9]] [3,3,2,1]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[9,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,9]=>[[1,4,7,9],[2,5,8],[3,6]] [3,3,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[9,8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8,9]=>[[1,4,7,8,9],[2,5],[3,6]] [3,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9]]=>[8,9,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,9,8]=>[[1,4,6,8],[2,5,7,9],[3]] [3,2,2,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9]]=>[9,8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8,9]=>[[1,4,6,8,9],[2,5,7],[3]] [3,2,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[9,8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8,9]=>[[1,4,6,7,8,9],[2,5],[3]] [3,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]] [2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]] [2,2,2,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8,9]=>[[1,3,5,7,8,9],[2,4,6]] [2,2,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]] [2,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[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]=>[1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9]] [10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] [9,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,10]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] [8,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,10,9]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] [8,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] [7,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[8,9,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,9,8]=>[[1,8],[2,9],[3,10],[4],[5],[6],[7]] [7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[10,8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8,10]=>[[1,8,10],[2,9],[3],[4],[5],[6],[7]] [7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]] [6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[10,7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7,10]=>[[1,7,10],[2,8],[3,9],[4],[5],[6]] [6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[9,10,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,10,9]=>[[1,7,9],[2,8,10],[3],[4],[5],[6]] [6,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[10,9,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,9,10]=>[[1,7,9,10],[2,8],[3],[4],[5],[6]] [6,1,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9,10]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]] [5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5,10]] [5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[10,6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6,10]=>[[1,6,10],[2,7],[3,8],[4,9],[5]] [5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[9,10,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,10,9]=>[[1,6,9],[2,7,10],[3,8],[4],[5]] [5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[10,9,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,9,10]=>[[1,6,9,10],[2,7],[3,8],[4],[5]] [5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,9,8,10]=>[[1,6,8,10],[2,7,9],[3],[4],[5]] [5,2,1,1,1]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[10,9,8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8,9,10]=>[[1,6,8,9,10],[2,7],[3],[4],[5]] [5,1,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]] [4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[9,10,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,10,9]=>[[1,5,9],[2,6,10],[3,7],[4,8]] [4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[10,9,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,9,10]=>[[1,5,9,10],[2,6],[3,7],[4,8]] [4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[8,9,10,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,10,9,8]=>[[1,5,8],[2,6,9],[3,7,10],[4]] [4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[10,8,9,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,9,8,10]=>[[1,5,8,10],[2,6,9],[3,7],[4]] [4,3,1,1,1]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[10,9,8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8,9,10]=>[[1,5,8,9,10],[2,6],[3,7],[4]] [4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,10,9]=>[[1,5,7,9],[2,6,8,10],[3],[4]] [4,2,2,1,1]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,9,10]=>[[1,5,7,9,10],[2,6,8],[3],[4]] [4,2,1,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[10,9,8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8,9,10]=>[[1,5,7,8,9,10],[2,6],[3],[4]] [4,1,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9,10]=>[[1,5,6,7,8,9,10],[2],[3],[4]] [3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[10,7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7,10]=>[[1,4,7,10],[2,5,8],[3,6,9]] [3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[9,10,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,10,9]=>[[1,4,7,9],[2,5,8,10],[3,6]] [3,3,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[10,9,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,9,10]=>[[1,4,7,9,10],[2,5,8],[3,6]] [3,3,1,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8,9,10]=>[[1,4,7,8,9,10],[2,5],[3,6]] [3,2,2,2,1]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,9,8,10]=>[[1,4,6,8,10],[2,5,7,9],[3]] [3,2,2,1,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[10,9,8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8,9,10]=>[[1,4,6,8,9,10],[2,5,7],[3]] [3,2,1,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8,9,10]=>[[1,4,6,7,8,9,10],[2,5],[3]] [3,1,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[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]=>[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]] [2,2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,9,10]=>[[1,3,5,7,9,10],[2,4,6,8]] [2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[10,9,8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8,9,10]=>[[1,3,5,7,8,9,10],[2,4,6]] [2,2,1,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8,9,10]=>[[1,3,5,6,7,8,9,10],[2,4]] [2,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[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]=>[1,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10]] [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]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[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]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] [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]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]] [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]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[[1,2,3,4,5,6,7,8,9,10,11,12]] []=>[]=>[]=>[]=>[]
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by 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.