Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1Cc0007;cc-rep-3
[1]=>[[1]]=>[1]=>[[1]] [2]=>[[1,2]]=>[1,2]=>[[1,2]] [1,1]=>[[1],[2]]=>[2,1]=>[[1],[2]] [3]=>[[1,2,3]]=>[1,2,3]=>[[1,2,3]] [2,1]=>[[1,2],[3]]=>[3,1,2]=>[[1,3],[2]] [1,1,1]=>[[1],[2],[3]]=>[3,2,1]=>[[1],[2],[3]] [4]=>[[1,2,3,4]]=>[1,2,3,4]=>[[1,2,3,4]] [3,1]=>[[1,2,3],[4]]=>[4,1,2,3]=>[[1,3,4],[2]] [2,2]=>[[1,2],[3,4]]=>[3,4,1,2]=>[[1,2],[3,4]] [2,1,1]=>[[1,2],[3],[4]]=>[4,3,1,2]=>[[1,4],[2],[3]] [1,1,1,1]=>[[1],[2],[3],[4]]=>[4,3,2,1]=>[[1],[2],[3],[4]] [5]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[[1,2,3,4,5]] [4,1]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[[1,3,4,5],[2]] [3,2]=>[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[[1,2,5],[3,4]] [3,1,1]=>[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[[1,4,5],[2],[3]] [2,2,1]=>[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[[1,3],[2,5],[4]] [2,1,1,1]=>[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[[1,5],[2],[3],[4]] [1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]] [6]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]] [5,1]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[[1,3,4,5,6],[2]] [4,2]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[[1,2,5,6],[3,4]] [4,1,1]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[[1,4,5,6],[2],[3]] [3,3]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[[1,2,3],[4,5,6]] [3,2,1]=>[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[[1,3,6],[2,5],[4]] [3,1,1,1]=>[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[[1,5,6],[2],[3],[4]] [2,2,2]=>[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[[1,2],[3,4],[5,6]] [2,2,1,1]=>[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[[1,4],[2,6],[3],[5]] [2,1,1,1,1]=>[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[[1,6],[2],[3],[4],[5]] [1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]] [7]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]] [6,1]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[[1,3,4,5,6,7],[2]] [5,2]=>[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[[1,2,5,6,7],[3,4]] [5,1,1]=>[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[[1,4,5,6,7],[2],[3]] [4,3]=>[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[[1,2,3,7],[4,5,6]] [4,2,1]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[[1,3,6,7],[2,5],[4]] [4,1,1,1]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[[1,5,6,7],[2],[3],[4]] [3,3,1]=>[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[[1,3,4],[2,6,7],[5]] [3,2,2]=>[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[[1,2,7],[3,4],[5,6]] [3,2,1,1]=>[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[[1,4,7],[2,6],[3],[5]] [3,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[[1,6,7],[2],[3],[4],[5]] [2,2,2,1]=>[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[[1,3],[2,5],[4,7],[6]] [2,2,1,1,1]=>[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[[1,5],[2,7],[3],[4],[6]] [2,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[[1,7],[2],[3],[4],[5],[6]] [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]] [8]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[[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]=>[[1,3,4,5,6,7,8],[2]] [6,2]=>[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[[1,2,5,6,7,8],[3,4]] [6,1,1]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[[1,4,5,6,7,8],[2],[3]] [5,3]=>[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[[1,2,3,7,8],[4,5,6]] [5,2,1]=>[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[[1,3,6,7,8],[2,5],[4]] [5,1,1,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[[1,5,6,7,8],[2],[3],[4]] [4,4]=>[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]] [4,3,1]=>[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[[1,3,4,8],[2,6,7],[5]] [4,2,2]=>[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[[1,2,7,8],[3,4],[5,6]] [4,2,1,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[[1,4,7,8],[2,6],[3],[5]] [4,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[[1,6,7,8],[2],[3],[4],[5]] [3,3,2]=>[[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[[1,2,5],[3,4,8],[6,7]] [3,3,1,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[[1,4,5],[2,7,8],[3],[6]] [3,2,2,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[[1,3,8],[2,5],[4,7],[6]] [3,2,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[8,7,6,4,5,1,2,3]=>[[1,5,8],[2,7],[3],[4],[6]] [3,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[[1,7,8],[2],[3],[4],[5],[6]] [2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]] [2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[[1,4],[2,6],[3,8],[5],[7]] [2,2,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[[1,6],[2,8],[3],[4],[5],[7]] [2,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[[1,8],[2],[3],[4],[5],[6],[7]] [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]] [9]=>[[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]] [8,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8,9],[2]] [7,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[[1,2,5,6,7,8,9],[3,4]] [7,1,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[[1,4,5,6,7,8,9],[2],[3]] [6,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[[1,2,3,7,8,9],[4,5,6]] [6,2,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[9,7,8,1,2,3,4,5,6]=>[[1,3,6,7,8,9],[2,5],[4]] [6,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[[1,5,6,7,8,9],[2],[3],[4]] [5,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[[1,2,3,4,9],[5,6,7,8]] [5,3,1]=>[[1,2,3,4,5],[6,7,8],[9]]=>[9,6,7,8,1,2,3,4,5]=>[[1,3,4,8,9],[2,6,7],[5]] [5,2,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[8,9,6,7,1,2,3,4,5]=>[[1,2,7,8,9],[3,4],[5,6]] [5,2,1,1]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[9,8,6,7,1,2,3,4,5]=>[[1,4,7,8,9],[2,6],[3],[5]] [5,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[[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]=>[[1,3,4,5],[2,7,8,9],[6]] [4,3,2]=>[[1,2,3,4],[5,6,7],[8,9]]=>[8,9,5,6,7,1,2,3,4]=>[[1,2,5,9],[3,4,8],[6,7]] [4,3,1,1]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[9,8,5,6,7,1,2,3,4]=>[[1,4,5,9],[2,7,8],[3],[6]] [4,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,1,2,3,4]=>[[1,3,8,9],[2,5],[4,7],[6]] [4,2,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,1,2,3,4]=>[[1,5,8,9],[2,7],[3],[4],[6]] [4,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7,8,9]] [3,3,2,1]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[9,7,8,4,5,6,1,2,3]=>[[1,3,6],[2,5,9],[4,8],[7]] [3,3,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[9,8,7,4,5,6,1,2,3]=>[[1,5,6],[2,8,9],[3],[4],[7]] [3,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9]]=>[8,9,6,7,4,5,1,2,3]=>[[1,2,9],[3,4],[5,6],[7,8]] [3,2,2,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9]]=>[9,8,6,7,4,5,1,2,3]=>[[1,4,9],[2,6],[3,8],[5],[7]] [3,2,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[9,8,7,6,4,5,1,2,3]=>[[1,6,9],[2,8],[3],[4],[5],[7]] [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]=>[[1,8,9],[2],[3],[4],[5],[6],[7]] [2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2]=>[[1,3],[2,5],[4,7],[6,9],[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]=>[[1,5],[2,7],[3,9],[4],[6],[8]] [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]=>[[1,7],[2,9],[3],[4],[5],[6],[8]] [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]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]] [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]] [10]=>[[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]] [9,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9,10],[2]] [8,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[[1,2,5,6,7,8,9,10],[3,4]] [8,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[[1,4,5,6,7,8,9,10],[2],[3]] [7,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[8,9,10,1,2,3,4,5,6,7]=>[[1,2,3,7,8,9,10],[4,5,6]] [7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[10,8,9,1,2,3,4,5,6,7]=>[[1,3,6,7,8,9,10],[2,5],[4]] [7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[[1,5,6,7,8,9,10],[2],[3],[4]] [6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[7,8,9,10,1,2,3,4,5,6]=>[[1,2,3,4,9,10],[5,6,7,8]] [6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[10,7,8,9,1,2,3,4,5,6]=>[[1,3,4,8,9,10],[2,6,7],[5]] [6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[9,10,7,8,1,2,3,4,5,6]=>[[1,2,7,8,9,10],[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]=>[[1,4,7,8,9,10],[2,6],[3],[5]] [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]=>[[1,6,7,8,9,10],[2],[3],[4],[5]] [5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9,10]] [5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[10,6,7,8,9,1,2,3,4,5]=>[[1,3,4,5,10],[2,7,8,9],[6]] [5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[9,10,6,7,8,1,2,3,4,5]=>[[1,2,5,9,10],[3,4,8],[6,7]] [5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[10,9,6,7,8,1,2,3,4,5]=>[[1,4,5,9,10],[2,7,8],[3],[6]] [5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,1,2,3,4,5]=>[[1,3,8,9,10],[2,5],[4,7],[6]] [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]=>[[1,5,8,9,10],[2,7],[3],[4],[6]] [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]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]] [4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[9,10,5,6,7,8,1,2,3,4]=>[[1,2,5,6],[3,4,9,10],[7,8]] [4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[10,9,5,6,7,8,1,2,3,4]=>[[1,4,5,6],[2,8,9,10],[3],[7]] [4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[8,9,10,5,6,7,1,2,3,4]=>[[1,2,3,10],[4,5,6],[7,8,9]] [4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[10,8,9,5,6,7,1,2,3,4]=>[[1,3,6,10],[2,5,9],[4,8],[7]] [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]=>[[1,5,6,10],[2,8,9],[3],[4],[7]] [4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,1,2,3,4]=>[[1,2,9,10],[3,4],[5,6],[7,8]] [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]=>[[1,4,9,10],[2,6],[3,8],[5],[7]] [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]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]] [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]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[10,7,8,9,4,5,6,1,2,3]=>[[1,3,4],[2,6,7],[5,9,10],[8]] [3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[9,10,7,8,4,5,6,1,2,3]=>[[1,2,7],[3,4,10],[5,6],[8,9]] [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]=>[[1,4,7],[2,6,10],[3,9],[5],[8]] [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]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]] [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]=>[[1,3,10],[2,5],[4,7],[6,9],[8]] [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]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]] [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]=>[[1,7,10],[2,9],[3],[4],[5],[6],[8]] [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]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] [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]=>[[1,2],[3,4],[5,6],[7,8],[9,10]] [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]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]] [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]=>[[1,6],[2,8],[3,10],[4],[5],[7],[9]] [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]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] [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]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] [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]] [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]=>[[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]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]] [6,4,2]=>[[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[11,12,7,8,9,10,1,2,3,4,5,6]=>[[1,2,5,6,11,12],[3,4,9,10],[7,8]] [4,4,2,2]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[11,12,9,10,5,6,7,8,1,2,3,4]=>[[1,2,7,8],[3,4,11,12],[5,6],[9,10]] [4,2,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,1,2,3,4]=>[[1,2,11,12],[3,4],[5,6],[7,8],[9,10]] [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]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] [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]] []=>[]=>[]=>[]
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
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.