Identifier
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1Cc0010;cc-rep-3
[1]=>[[1]]=>[1]=>[.,.] [2]=>[[1,2]]=>[1,2]=>[.,[.,.]] [1,1]=>[[1],[2]]=>[2,1]=>[[.,.],.] [3]=>[[1,2,3]]=>[1,2,3]=>[.,[.,[.,.]]] [2,1]=>[[1,3],[2]]=>[2,1,3]=>[[.,.],[.,.]] [1,1,1]=>[[1],[2],[3]]=>[3,2,1]=>[[[.,.],.],.] [4]=>[[1,2,3,4]]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [3,1]=>[[1,3,4],[2]]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [2,2]=>[[1,2],[3,4]]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [2,1,1]=>[[1,4],[2],[3]]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,1,1,1]=>[[1],[2],[3],[4]]=>[4,3,2,1]=>[[[[.,.],.],.],.] [5]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [4,1]=>[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [3,2]=>[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]] [3,1,1]=>[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [2,2,1]=>[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]] [2,1,1,1]=>[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [6]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [5,1]=>[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [4,2]=>[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [4,1,1]=>[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [3,3]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [3,2,1]=>[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]] [3,1,1,1]=>[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [2,2,2]=>[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [2,2,1,1]=>[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [2,1,1,1,1]=>[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [7]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [6,1]=>[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [5,2]=>[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [5,1,1]=>[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [4,3]=>[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [4,2,1]=>[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [4,1,1,1]=>[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [3,3,1]=>[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [3,2,2]=>[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [3,2,1,1]=>[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [3,1,1,1,1]=>[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [2,2,2,1]=>[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [2,2,1,1,1]=>[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [2,1,1,1,1,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [8]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [7,1]=>[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [6,2]=>[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [6,1,1]=>[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [5,3]=>[[1,2,3,7,8],[4,5,6]]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [5,2,1]=>[[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [5,1,1,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] [4,4]=>[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [4,3,1]=>[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] [4,2,2]=>[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] [4,2,1,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] [4,1,1,1,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]] [3,3,2]=>[[1,2,5],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] [3,3,1,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] [3,2,2,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] [3,2,1,1,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]] [3,1,1,1,1,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]] [2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] [2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]] [2,2,1,1,1,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]] [2,1,1,1,1,1,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]] [1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [9]=>[[1,2,3,4,5,6,7,8,9]]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [8,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [7,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [7,1,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [6,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[4,5,6,1,2,3,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] [6,2,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] [6,1,1,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] [5,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [5,3,1]=>[[1,3,4,8,9],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]] [5,2,2]=>[[1,2,7,8,9],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]] [5,2,1,1]=>[[1,4,7,8,9],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] [5,1,1,1,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] [4,4,1]=>[[1,3,4,5],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] [4,3,2]=>[[1,2,5,9],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]] [4,3,1,1]=>[[1,4,5,9],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9]=>[[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]] [4,2,2,1]=>[[1,3,8,9],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9]=>[[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]] [4,2,1,1,1]=>[[1,5,8,9],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] [4,1,1,1,1,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] [3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]] [3,3,2,1]=>[[1,3,6],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,.]]] [3,3,1,1,1]=>[[1,5,6],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]] [3,2,2,2]=>[[1,2,9],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]] [3,2,2,1,1]=>[[1,4,9],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9]=>[[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]] [3,2,1,1,1,1]=>[[1,6,9],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] [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]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] [2,2,2,2,1]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]] [2,2,2,1,1,1]=>[[1,5],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]] [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]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] [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]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] [1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.] [10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] [9,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [8,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [8,1,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [7,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[4,5,6,1,2,3,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] [7,2,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9,10]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [7,1,1,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [6,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] [6,3,1]=>[[1,3,4,8,9,10],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9,10]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] [6,2,2]=>[[1,2,7,8,9,10],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9,10]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]] [6,2,1,1]=>[[1,4,7,8,9,10],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9,10]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] [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]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] [5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] [5,4,1]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5,10]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [5,3,2]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9,10]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,[.,.]]]]] [5,3,1,1]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9,10]=>[[[[.,.],.],[.,[.,.]]],[.,[.,[.,[.,.]]]]] [5,2,2,1]=>[[1,3,8,9,10],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9,10]=>[[[[.,.],[.,.]],[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,[.,.]]]]] [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]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] [4,4,2]=>[[1,2,5,6],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]] [4,4,1,1]=>[[1,4,5,6],[2,8,9,10],[3],[7]]=>[7,3,2,8,9,10,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] [4,3,3]=>[[1,2,3,10],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3,10]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]] [4,3,2,1]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6,10]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,[.,[.,.]]]] [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]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,[.,.]]]] [4,2,2,2]=>[[1,2,9,10],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9,10]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]] [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]=>[[[[[.,.],.],[.,.]],[.,.]],[.,[.,[.,.]]]] [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]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,[.,.]]]] [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]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] [3,3,3,1]=>[[1,3,4],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]] [3,3,2,2]=>[[1,2,7],[3,4,10],[5,6],[8,9]]=>[8,9,5,6,3,4,10,1,2,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]] [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]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],[.,[.,.]]] [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]=>[[[[[[.,.],.],.],.],[.,[.,.]]],[.,[.,.]]] [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]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]] [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]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,[.,.]]] [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]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,[.,.]]] [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]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] [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]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] [2,2,2,2,1,1]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[9,7,5,10,3,8,2,6,1,4]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]] [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]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]] [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]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] [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]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] [1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] [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]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]] [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]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] [1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.] []=>[]=>[]=>.
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
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.