Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1Cc0002;cc-rep-4
[1]=>[[1]]=>[1]=>[1]=>[1] [2]=>[[1,2]]=>[1,2]=>[1,2]=>[2] [1,1]=>[[1],[2]]=>[2,1]=>[2,1]=>[1,1] [3]=>[[1,2,3]]=>[1,2,3]=>[1,2,3]=>[3] [2,1]=>[[1,2],[3]]=>[3,1,2]=>[1,3,2]=>[2,1] [1,1,1]=>[[1],[2],[3]]=>[3,2,1]=>[3,2,1]=>[1,1,1] [4]=>[[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[4] [3,1]=>[[1,2,3],[4]]=>[4,1,2,3]=>[1,2,4,3]=>[3,1] [2,2]=>[[1,2],[3,4]]=>[3,4,1,2]=>[3,1,4,2]=>[2,2] [2,1,1]=>[[1,2],[3],[4]]=>[4,3,1,2]=>[1,4,3,2]=>[2,1,1] [1,1,1,1]=>[[1],[2],[3],[4]]=>[4,3,2,1]=>[4,3,2,1]=>[1,1,1,1] [5]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5] [4,1]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[1,2,3,5,4]=>[4,1] [3,2]=>[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[1,4,2,5,3]=>[3,2] [3,1,1]=>[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[3,1,1] [2,2,1]=>[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[3,1,5,4,2]=>[2,2,1] [2,1,1,1]=>[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[1,5,4,3,2]=>[2,1,1,1] [1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,1,1,1,1] [6]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6] [5,1]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>[5,1] [4,2]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[1,2,5,3,6,4]=>[4,2] [4,1,1]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>[4,1,1] [3,3]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>[3,3] [3,2,1]=>[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[1,4,2,6,5,3]=>[3,2,1] [3,1,1,1]=>[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>[3,1,1,1] [2,2,2]=>[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[5,3,1,6,4,2]=>[2,2,2] [2,2,1,1]=>[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[3,1,6,5,4,2]=>[2,2,1,1] [2,1,1,1,1]=>[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>[2,1,1,1,1] [1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[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]=>[1,2,3,4,5,6,7]=>[7] [6,1]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>[6,1] [5,2]=>[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[1,2,3,6,4,7,5]=>[5,2] [5,1,1]=>[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>[5,1,1] [4,3]=>[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[1,5,2,6,3,7,4]=>[4,3] [4,2,1]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[1,2,5,3,7,6,4]=>[4,2,1] [4,1,1,1]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[4,1,1,1] [3,3,1]=>[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[4,1,5,2,7,6,3]=>[3,3,1] [3,2,2]=>[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[1,6,4,2,7,5,3]=>[3,2,2] [3,2,1,1]=>[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[1,4,2,7,6,5,3]=>[3,2,1,1] [3,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1] [2,2,2,1]=>[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[5,3,1,7,6,4,2]=>[2,2,2,1] [2,2,1,1,1]=>[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[3,1,7,6,5,4,2]=>[2,2,1,1,1] [2,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1] [1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[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]=>[1,2,3,4,5,6,7,8]=>[8] [7,1]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>[7,1] [6,2]=>[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,7,5,8,6]=>[6,2] [6,1,1]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>[6,1,1] [5,3]=>[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[1,2,6,3,7,4,8,5]=>[5,3] [5,2,1]=>[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[1,2,3,6,4,8,7,5]=>[5,2,1] [5,1,1,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1] [4,4]=>[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>[4,4] [4,3,1]=>[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[1,5,2,6,3,8,7,4]=>[4,3,1] [4,2,2]=>[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[1,2,7,5,3,8,6,4]=>[4,2,2] [4,2,1,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[1,2,5,3,8,7,6,4]=>[4,2,1,1] [4,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1] [3,3,2]=>[[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[4,1,7,5,2,8,6,3]=>[3,3,2] [3,3,1,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[4,1,5,2,8,7,6,3]=>[3,3,1,1] [3,2,2,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[1,6,4,2,8,7,5,3]=>[3,2,2,1] [3,2,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[8,7,6,4,5,1,2,3]=>[1,4,2,8,7,6,5,3]=>[3,2,1,1,1] [3,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1] [2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[7,5,3,1,8,6,4,2]=>[2,2,2,2] [2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[5,3,1,8,7,6,4,2]=>[2,2,2,1,1] [2,2,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[3,1,8,7,6,5,4,2]=>[2,2,1,1,1,1] [2,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1] [1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[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]=>[1,2,3,4,5,6,7,8,9]=>[9] [8,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>[8,1] [7,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,8,6,9,7]=>[7,2] [7,1,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>[7,1,1] [6,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[1,2,3,7,4,8,5,9,6]=>[6,3] [6,2,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,7,5,9,8,6]=>[6,2,1] [6,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>[6,1,1,1] [5,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[1,6,2,7,3,8,4,9,5]=>[5,4] [5,3,1]=>[[1,2,3,4,5],[6,7,8],[9]]=>[9,6,7,8,1,2,3,4,5]=>[1,2,6,3,7,4,9,8,5]=>[5,3,1] [5,2,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[8,9,6,7,1,2,3,4,5]=>[1,2,3,8,6,4,9,7,5]=>[5,2,2] [5,2,1,1]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[9,8,6,7,1,2,3,4,5]=>[1,2,3,6,4,9,8,7,5]=>[5,2,1,1] [5,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[5,1,1,1,1] [4,4,1]=>[[1,2,3,4],[5,6,7,8],[9]]=>[9,5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,9,8,4]=>[4,4,1] [4,3,2]=>[[1,2,3,4],[5,6,7],[8,9]]=>[8,9,5,6,7,1,2,3,4]=>[1,5,2,8,6,3,9,7,4]=>[4,3,2] [4,3,1,1]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[9,8,5,6,7,1,2,3,4]=>[1,5,2,6,3,9,8,7,4]=>[4,3,1,1] [4,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,1,2,3,4]=>[1,2,7,5,3,9,8,6,4]=>[4,2,2,1] [4,2,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,1,2,3,4]=>[1,2,5,3,9,8,7,6,4]=>[4,2,1,1,1] [4,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>[4,1,1,1,1,1] [3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[7,4,1,8,5,2,9,6,3]=>[3,3,3] [3,3,2,1]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[9,7,8,4,5,6,1,2,3]=>[4,1,7,5,2,9,8,6,3]=>[3,3,2,1] [3,3,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[9,8,7,4,5,6,1,2,3]=>[4,1,5,2,9,8,7,6,3]=>[3,3,1,1,1] [3,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9]]=>[8,9,6,7,4,5,1,2,3]=>[1,8,6,4,2,9,7,5,3]=>[3,2,2,2] [3,2,2,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9]]=>[9,8,6,7,4,5,1,2,3]=>[1,6,4,2,9,8,7,5,3]=>[3,2,2,1,1] [3,2,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[9,8,7,6,4,5,1,2,3]=>[1,4,2,9,8,7,6,5,3]=>[3,2,1,1,1,1] [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]=>[1,2,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1] [2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2]=>[7,5,3,1,9,8,6,4,2]=>[2,2,2,2,1] [2,2,2,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,3,4,1,2]=>[5,3,1,9,8,7,6,4,2]=>[2,2,2,1,1,1] [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]=>[3,1,9,8,7,6,5,4,2]=>[2,2,1,1,1,1,1] [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]=>[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1] [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]=>[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]=>[1,2,3,4,5,6,7,8,9,10]=>[10] [9,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>[9,1] [8,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,9,7,10,8]=>[8,2] [8,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>[8,1,1] [7,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,8,5,9,6,10,7]=>[7,3] [7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[10,8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,8,6,10,9,7]=>[7,2,1] [7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>[7,1,1,1] [6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[7,8,9,10,1,2,3,4,5,6]=>[1,2,7,3,8,4,9,5,10,6]=>[6,4] [6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[10,7,8,9,1,2,3,4,5,6]=>[1,2,3,7,4,8,5,10,9,6]=>[6,3,1] [6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[9,10,7,8,1,2,3,4,5,6]=>[1,2,3,4,9,7,5,10,8,6]=>[6,2,2] [6,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[10,9,7,8,1,2,3,4,5,6]=>[1,2,3,4,7,5,10,9,8,6]=>[6,2,1,1] [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]=>[1,2,3,4,5,10,9,8,7,6]=>[6,1,1,1,1] [5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[6,1,7,2,8,3,9,4,10,5]=>[5,5] [5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[10,6,7,8,9,1,2,3,4,5]=>[1,6,2,7,3,8,4,10,9,5]=>[5,4,1] [5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[9,10,6,7,8,1,2,3,4,5]=>[1,2,6,3,9,7,4,10,8,5]=>[5,3,2] [5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[10,9,6,7,8,1,2,3,4,5]=>[1,2,6,3,7,4,10,9,8,5]=>[5,3,1,1] [5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,1,2,3,4,5]=>[1,2,3,8,6,4,10,9,7,5]=>[5,2,2,1] [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]=>[1,2,3,6,4,10,9,8,7,5]=>[5,2,1,1,1] [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]=>[1,2,3,4,10,9,8,7,6,5]=>[5,1,1,1,1,1] [4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[9,10,5,6,7,8,1,2,3,4]=>[5,1,6,2,9,7,3,10,8,4]=>[4,4,2] [4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[10,9,5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,10,9,8,4]=>[4,4,1,1] [4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[8,9,10,5,6,7,1,2,3,4]=>[1,8,5,2,9,6,3,10,7,4]=>[4,3,3] [4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[10,8,9,5,6,7,1,2,3,4]=>[1,5,2,8,6,3,10,9,7,4]=>[4,3,2,1] [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]=>[1,5,2,6,3,10,9,8,7,4]=>[4,3,1,1,1] [4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,1,2,3,4]=>[1,2,9,7,5,3,10,8,6,4]=>[4,2,2,2] [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]=>[1,2,7,5,3,10,9,8,6,4]=>[4,2,2,1,1] [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]=>[1,2,5,3,10,9,8,7,6,4]=>[4,2,1,1,1,1] [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]=>[1,2,3,10,9,8,7,6,5,4]=>[4,1,1,1,1,1,1] [3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[10,7,8,9,4,5,6,1,2,3]=>[7,4,1,8,5,2,10,9,6,3]=>[3,3,3,1] [3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[9,10,7,8,4,5,6,1,2,3]=>[4,1,9,7,5,2,10,8,6,3]=>[3,3,2,2] [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]=>[4,1,7,5,2,10,9,8,6,3]=>[3,3,2,1,1] [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]=>[4,1,5,2,10,9,8,7,6,3]=>[3,3,1,1,1,1] [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]=>[1,8,6,4,2,10,9,7,5,3]=>[3,2,2,2,1] [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]=>[1,6,4,2,10,9,8,7,5,3]=>[3,2,2,1,1,1] [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]=>[1,4,2,10,9,8,7,6,5,3]=>[3,2,1,1,1,1,1] [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]=>[1,2,10,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1,1] [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]=>[9,7,5,3,1,10,8,6,4,2]=>[2,2,2,2,2] [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]=>[7,5,3,1,10,9,8,6,4,2]=>[2,2,2,2,1,1] [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]=>[5,3,1,10,9,8,7,6,4,2]=>[2,2,2,1,1,1,1] [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]=>[3,1,10,9,8,7,6,5,4,2]=>[2,2,1,1,1,1,1,1] [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]=>[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1] [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]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1] [6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[6,6] [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]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1] []=>[]=>[]=>[]=>[]
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
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
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
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 the shape of its corresponding insertion and recording tableau.