Processing math: 100%

Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ 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] => [[1,2],[3]] => [3,1,2] => [[.,.],[.,.]]
[1,1,1] => [[1],[2],[3]] => [3,2,1] => [[[.,.],.],.]
[4] => [[1,2,3,4]] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[3,1] => [[1,2,3],[4]] => [4,1,2,3] => [[.,.],[.,[.,.]]]
[2,2] => [[1,2],[3,4]] => [3,4,1,2] => [[.,[.,.]],[.,.]]
[2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => [[[.,.],.],[.,.]]
[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] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
[3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]]
[3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]]
[2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => [[[.,.],[.,.]],[.,.]]
[2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]]
[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] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
[4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]]
[4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]]
[3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]]
[3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]]
[3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]]
[2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]]
[2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [[[[.,.],.],[.,.]],[.,.]]
[2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]]
[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] => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[5,2] => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[5,1,1] => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[4,3] => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[4,2,1] => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[3,3,1] => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[3,2,2] => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]]
[2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]]
[2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]]
[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] => [[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[6,2] => [[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[6,1,1] => [[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[5,3] => [[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[5,2,1] => [[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[4,4] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[4,3,1] => [[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[4,2,2] => [[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[3,3,2] => [[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[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] => [[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[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] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[7,2] => [[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[6,3] => [[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[5,4] => [[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => [[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]]
[4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => [[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]]
[4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => [[[[.,.],[.,.]],[.,[.,.]]],[.,[.,.]]]
[3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => [[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]]
[3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => [[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]]
[3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => [[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1] => [[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] => [[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
>>> Load all 142 entries. <<<
[7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => [[[[.,.],.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,1,2,3,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]
[4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => [[[[.,.],[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[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] => [[[[[.,.],.],.],[.,[.,.]]],[.,[.,[.,.]]]]
[4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[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] => [[[[[.,.],.],[.,.]],[.,.]],[.,[.,[.,.]]]]
[4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,[.,.]]]]
[4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]
[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] => [[[[[.,.],.],[.,.]],[.,[.,.]]],[.,[.,.]]]
[3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => [[[[[[.,.],.],.],.],[.,[.,.]]],[.,[.,.]]]
[3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => [[[[[[.,.],.],.],[.,.]],[.,.]],[.,[.,.]]]
[3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,[.,.]]]
[3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[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] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => [[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[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] => [[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]
[2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1] => [[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
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
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 σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.