Identifier
Mp00045:
Integer partitions
—reading tableau⟶
Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[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] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
>>> Load all 143 entries. <<<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
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
Sorry, this map was not found in the database.