Processing math: 100%

Identifier
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
[1,0] => [[1],[2]] => [2,1] => [1,2] => [.,[.,.]]
[1,0,1,0] => [[1,3],[2,4]] => [2,4,1,3] => [3,1,4,2] => [[.,.],[[.,.],.]]
[1,1,0,0] => [[1,2],[3,4]] => [3,4,1,2] => [2,1,4,3] => [[.,.],[[.,.],.]]
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [5,2,1,6,4,3] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [4,3,1,6,5,2] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [[[.,.],.],[[[.,.],.],.]]
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => [7,5,3,1,8,6,4,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => [7,5,2,1,8,6,4,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [2,5,6,8,1,3,4,7] => [7,4,3,1,8,6,5,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [2,5,7,8,1,3,4,6] => [7,4,2,1,8,6,5,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [2,6,7,8,1,3,4,5] => [7,3,2,1,8,6,5,4] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => [6,5,3,1,8,7,4,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [3,4,7,8,1,2,5,6] => [6,5,2,1,8,7,4,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => [6,4,3,1,8,7,5,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => [6,4,2,1,8,7,5,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => [6,3,2,1,8,7,5,4] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => [5,4,3,1,8,7,6,2] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [5,4,2,1,8,7,6,3] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [4,6,7,8,1,2,3,5] => [5,3,2,1,8,7,6,4] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => [2,4,6,8,10,1,3,5,7,9] => [9,7,5,3,1,10,8,6,4,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => [2,4,6,9,10,1,3,5,7,8] => [9,7,5,2,1,10,8,6,4,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => [2,4,7,8,10,1,3,5,6,9] => [9,7,4,3,1,10,8,6,5,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => [2,4,7,9,10,1,3,5,6,8] => [9,7,4,2,1,10,8,6,5,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => [2,4,8,9,10,1,3,5,6,7] => [9,7,3,2,1,10,8,6,5,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => [2,5,6,8,10,1,3,4,7,9] => [9,6,5,3,1,10,8,7,4,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => [2,5,6,9,10,1,3,4,7,8] => [9,6,5,2,1,10,8,7,4,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => [2,5,7,8,10,1,3,4,6,9] => [9,6,4,3,1,10,8,7,5,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => [2,5,7,9,10,1,3,4,6,8] => [9,6,4,2,1,10,8,7,5,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => [2,5,8,9,10,1,3,4,6,7] => [9,6,3,2,1,10,8,7,5,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => [2,6,7,8,10,1,3,4,5,9] => [9,5,4,3,1,10,8,7,6,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => [2,6,7,9,10,1,3,4,5,8] => [9,5,4,2,1,10,8,7,6,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => [2,6,8,9,10,1,3,4,5,7] => [9,5,3,2,1,10,8,7,6,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => [2,7,8,9,10,1,3,4,5,6] => [9,4,3,2,1,10,8,7,6,5] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => [3,4,6,8,10,1,2,5,7,9] => [8,7,5,3,1,10,9,6,4,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => [3,4,6,9,10,1,2,5,7,8] => [8,7,5,2,1,10,9,6,4,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => [3,4,7,8,10,1,2,5,6,9] => [8,7,4,3,1,10,9,6,5,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => [3,4,7,9,10,1,2,5,6,8] => [8,7,4,2,1,10,9,6,5,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => [3,4,8,9,10,1,2,5,6,7] => [8,7,3,2,1,10,9,6,5,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => [3,5,6,8,10,1,2,4,7,9] => [8,6,5,3,1,10,9,7,4,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => [3,5,6,9,10,1,2,4,7,8] => [8,6,5,2,1,10,9,7,4,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => [3,5,7,8,10,1,2,4,6,9] => [8,6,4,3,1,10,9,7,5,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => [3,5,7,9,10,1,2,4,6,8] => [8,6,4,2,1,10,9,7,5,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => [3,5,8,9,10,1,2,4,6,7] => [8,6,3,2,1,10,9,7,5,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => [3,6,7,8,10,1,2,4,5,9] => [8,5,4,3,1,10,9,7,6,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => [3,6,7,9,10,1,2,4,5,8] => [8,5,4,2,1,10,9,7,6,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => [3,6,8,9,10,1,2,4,5,7] => [8,5,3,2,1,10,9,7,6,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => [3,7,8,9,10,1,2,4,5,6] => [8,4,3,2,1,10,9,7,6,5] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => [4,5,6,8,10,1,2,3,7,9] => [7,6,5,3,1,10,9,8,4,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => [4,5,6,9,10,1,2,3,7,8] => [7,6,5,2,1,10,9,8,4,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => [4,5,7,8,10,1,2,3,6,9] => [7,6,4,3,1,10,9,8,5,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => [4,5,7,9,10,1,2,3,6,8] => [7,6,4,2,1,10,9,8,5,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => [4,5,8,9,10,1,2,3,6,7] => [7,6,3,2,1,10,9,8,5,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => [4,6,7,8,10,1,2,3,5,9] => [7,5,4,3,1,10,9,8,6,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => [4,6,7,9,10,1,2,3,5,8] => [7,5,4,2,1,10,9,8,6,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => [4,6,8,9,10,1,2,3,5,7] => [7,5,3,2,1,10,9,8,6,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => [4,7,8,9,10,1,2,3,5,6] => [7,4,3,2,1,10,9,8,6,5] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => [5,6,7,8,10,1,2,3,4,9] => [6,5,4,3,1,10,9,8,7,2] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => [5,6,7,9,10,1,2,3,4,8] => [6,5,4,2,1,10,9,8,7,3] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => [5,6,8,9,10,1,2,3,4,7] => [6,5,3,2,1,10,9,8,7,4] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => [5,7,8,9,10,1,2,3,4,6] => [6,4,3,2,1,10,9,8,7,5] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [2,4,6,8,10,12,1,3,5,7,9,11] => [11,9,7,5,3,1,12,10,8,6,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => [2,4,6,8,11,12,1,3,5,7,9,10] => [11,9,7,5,2,1,12,10,8,6,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => [2,4,6,9,10,12,1,3,5,7,8,11] => [11,9,7,4,3,1,12,10,8,6,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => [2,4,6,9,11,12,1,3,5,7,8,10] => [11,9,7,4,2,1,12,10,8,6,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => [2,4,6,10,11,12,1,3,5,7,8,9] => [11,9,7,3,2,1,12,10,8,6,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => [2,4,7,8,10,12,1,3,5,6,9,11] => [11,9,6,5,3,1,12,10,8,7,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => [2,4,7,8,11,12,1,3,5,6,9,10] => [11,9,6,5,2,1,12,10,8,7,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => [2,4,7,9,10,12,1,3,5,6,8,11] => [11,9,6,4,3,1,12,10,8,7,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => [2,4,7,9,11,12,1,3,5,6,8,10] => [11,9,6,4,2,1,12,10,8,7,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => [2,4,7,10,11,12,1,3,5,6,8,9] => [11,9,6,3,2,1,12,10,8,7,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => [2,4,8,9,10,12,1,3,5,6,7,11] => [11,9,5,4,3,1,12,10,8,7,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => [2,4,8,9,11,12,1,3,5,6,7,10] => [11,9,5,4,2,1,12,10,8,7,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => [2,4,8,10,11,12,1,3,5,6,7,9] => [11,9,5,3,2,1,12,10,8,7,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => [2,4,9,10,11,12,1,3,5,6,7,8] => [11,9,4,3,2,1,12,10,8,7,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => [2,5,6,8,10,12,1,3,4,7,9,11] => [11,8,7,5,3,1,12,10,9,6,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => [2,5,6,8,11,12,1,3,4,7,9,10] => [11,8,7,5,2,1,12,10,9,6,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => [2,5,6,9,10,12,1,3,4,7,8,11] => [11,8,7,4,3,1,12,10,9,6,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => [2,5,6,9,11,12,1,3,4,7,8,10] => [11,8,7,4,2,1,12,10,9,6,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => [2,5,6,10,11,12,1,3,4,7,8,9] => [11,8,7,3,2,1,12,10,9,6,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => [2,5,7,8,10,12,1,3,4,6,9,11] => [11,8,6,5,3,1,12,10,9,7,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => [2,5,7,8,11,12,1,3,4,6,9,10] => [11,8,6,5,2,1,12,10,9,7,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => [2,5,7,9,10,12,1,3,4,6,8,11] => [11,8,6,4,3,1,12,10,9,7,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => [2,5,7,9,11,12,1,3,4,6,8,10] => [11,8,6,4,2,1,12,10,9,7,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => [2,5,7,10,11,12,1,3,4,6,8,9] => [11,8,6,3,2,1,12,10,9,7,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => [2,5,8,9,10,12,1,3,4,6,7,11] => [11,8,5,4,3,1,12,10,9,7,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => [2,5,8,9,11,12,1,3,4,6,7,10] => [11,8,5,4,2,1,12,10,9,7,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => [2,5,8,10,11,12,1,3,4,6,7,9] => [11,8,5,3,2,1,12,10,9,7,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => [2,5,9,10,11,12,1,3,4,6,7,8] => [11,8,4,3,2,1,12,10,9,7,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => [2,6,7,8,10,12,1,3,4,5,9,11] => [11,7,6,5,3,1,12,10,9,8,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => [2,6,7,8,11,12,1,3,4,5,9,10] => [11,7,6,5,2,1,12,10,9,8,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => [2,6,7,9,10,12,1,3,4,5,8,11] => [11,7,6,4,3,1,12,10,9,8,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => [2,6,7,9,11,12,1,3,4,5,8,10] => [11,7,6,4,2,1,12,10,9,8,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => [2,6,7,10,11,12,1,3,4,5,8,9] => [11,7,6,3,2,1,12,10,9,8,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => [2,6,8,9,10,12,1,3,4,5,7,11] => [11,7,5,4,3,1,12,10,9,8,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => [2,6,8,9,11,12,1,3,4,5,7,10] => [11,7,5,4,2,1,12,10,9,8,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => [2,6,8,10,11,12,1,3,4,5,7,9] => [11,7,5,3,2,1,12,10,9,8,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => [2,6,9,10,11,12,1,3,4,5,7,8] => [11,7,4,3,2,1,12,10,9,8,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => [2,7,8,9,10,12,1,3,4,5,6,11] => [11,6,5,4,3,1,12,10,9,8,7,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => [2,7,8,9,11,12,1,3,4,5,6,10] => [11,6,5,4,2,1,12,10,9,8,7,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => [2,7,8,10,11,12,1,3,4,5,6,9] => [11,6,5,3,2,1,12,10,9,8,7,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => [2,7,9,10,11,12,1,3,4,5,6,8] => [11,6,4,3,2,1,12,10,9,8,7,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => [2,8,9,10,11,12,1,3,4,5,6,7] => [11,5,4,3,2,1,12,10,9,8,7,6] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => [3,4,6,8,10,12,1,2,5,7,9,11] => [10,9,7,5,3,1,12,11,8,6,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => [3,4,6,8,11,12,1,2,5,7,9,10] => [10,9,7,5,2,1,12,11,8,6,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => [3,4,6,9,10,12,1,2,5,7,8,11] => [10,9,7,4,3,1,12,11,8,6,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => [3,4,6,9,11,12,1,2,5,7,8,10] => [10,9,7,4,2,1,12,11,8,6,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => [3,4,6,10,11,12,1,2,5,7,8,9] => [10,9,7,3,2,1,12,11,8,6,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => [3,4,7,8,10,12,1,2,5,6,9,11] => [10,9,6,5,3,1,12,11,8,7,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => [3,4,7,8,11,12,1,2,5,6,9,10] => [10,9,6,5,2,1,12,11,8,7,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => [3,4,7,9,10,12,1,2,5,6,8,11] => [10,9,6,4,3,1,12,11,8,7,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => [3,4,7,9,11,12,1,2,5,6,8,10] => [10,9,6,4,2,1,12,11,8,7,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => [3,4,7,10,11,12,1,2,5,6,8,9] => [10,9,6,3,2,1,12,11,8,7,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => [3,4,8,9,10,12,1,2,5,6,7,11] => [10,9,5,4,3,1,12,11,8,7,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => [3,4,8,9,11,12,1,2,5,6,7,10] => [10,9,5,4,2,1,12,11,8,7,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => [3,4,8,10,11,12,1,2,5,6,7,9] => [10,9,5,3,2,1,12,11,8,7,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => [3,4,9,10,11,12,1,2,5,6,7,8] => [10,9,4,3,2,1,12,11,8,7,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => [3,5,6,8,10,12,1,2,4,7,9,11] => [10,8,7,5,3,1,12,11,9,6,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => [3,5,6,8,11,12,1,2,4,7,9,10] => [10,8,7,5,2,1,12,11,9,6,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => [3,5,6,9,10,12,1,2,4,7,8,11] => [10,8,7,4,3,1,12,11,9,6,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => [3,5,6,9,11,12,1,2,4,7,8,10] => [10,8,7,4,2,1,12,11,9,6,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => [3,5,6,10,11,12,1,2,4,7,8,9] => [10,8,7,3,2,1,12,11,9,6,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => [3,5,7,8,10,12,1,2,4,6,9,11] => [10,8,6,5,3,1,12,11,9,7,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => [3,5,7,8,11,12,1,2,4,6,9,10] => [10,8,6,5,2,1,12,11,9,7,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => [3,5,7,9,10,12,1,2,4,6,8,11] => [10,8,6,4,3,1,12,11,9,7,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => [3,5,7,9,11,12,1,2,4,6,8,10] => [10,8,6,4,2,1,12,11,9,7,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => [3,5,7,10,11,12,1,2,4,6,8,9] => [10,8,6,3,2,1,12,11,9,7,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => [3,5,8,9,10,12,1,2,4,6,7,11] => [10,8,5,4,3,1,12,11,9,7,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => [3,5,8,9,11,12,1,2,4,6,7,10] => [10,8,5,4,2,1,12,11,9,7,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => [3,5,8,10,11,12,1,2,4,6,7,9] => [10,8,5,3,2,1,12,11,9,7,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => [3,5,9,10,11,12,1,2,4,6,7,8] => [10,8,4,3,2,1,12,11,9,7,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => [3,6,7,8,10,12,1,2,4,5,9,11] => [10,7,6,5,3,1,12,11,9,8,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => [3,6,7,8,11,12,1,2,4,5,9,10] => [10,7,6,5,2,1,12,11,9,8,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => [3,6,7,9,10,12,1,2,4,5,8,11] => [10,7,6,4,3,1,12,11,9,8,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => [3,6,7,9,11,12,1,2,4,5,8,10] => [10,7,6,4,2,1,12,11,9,8,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => [3,6,7,10,11,12,1,2,4,5,8,9] => [10,7,6,3,2,1,12,11,9,8,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => [3,6,8,9,10,12,1,2,4,5,7,11] => [10,7,5,4,3,1,12,11,9,8,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => [3,6,8,9,11,12,1,2,4,5,7,10] => [10,7,5,4,2,1,12,11,9,8,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => [3,6,8,10,11,12,1,2,4,5,7,9] => [10,7,5,3,2,1,12,11,9,8,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => [3,6,9,10,11,12,1,2,4,5,7,8] => [10,7,4,3,2,1,12,11,9,8,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => [3,7,8,9,10,12,1,2,4,5,6,11] => [10,6,5,4,3,1,12,11,9,8,7,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => [3,7,8,9,11,12,1,2,4,5,6,10] => [10,6,5,4,2,1,12,11,9,8,7,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => [3,7,8,10,11,12,1,2,4,5,6,9] => [10,6,5,3,2,1,12,11,9,8,7,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => [3,7,9,10,11,12,1,2,4,5,6,8] => [10,6,4,3,2,1,12,11,9,8,7,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => [3,8,9,10,11,12,1,2,4,5,6,7] => [10,5,4,3,2,1,12,11,9,8,7,6] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => [4,5,6,8,10,12,1,2,3,7,9,11] => [9,8,7,5,3,1,12,11,10,6,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => [4,5,6,8,11,12,1,2,3,7,9,10] => [9,8,7,5,2,1,12,11,10,6,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => [4,5,6,9,10,12,1,2,3,7,8,11] => [9,8,7,4,3,1,12,11,10,6,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => [4,5,6,9,11,12,1,2,3,7,8,10] => [9,8,7,4,2,1,12,11,10,6,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => [4,5,6,10,11,12,1,2,3,7,8,9] => [9,8,7,3,2,1,12,11,10,6,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => [4,5,7,8,10,12,1,2,3,6,9,11] => [9,8,6,5,3,1,12,11,10,7,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => [4,5,7,8,11,12,1,2,3,6,9,10] => [9,8,6,5,2,1,12,11,10,7,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => [4,5,7,9,10,12,1,2,3,6,8,11] => [9,8,6,4,3,1,12,11,10,7,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => [4,5,7,9,11,12,1,2,3,6,8,10] => [9,8,6,4,2,1,12,11,10,7,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => [4,5,7,10,11,12,1,2,3,6,8,9] => [9,8,6,3,2,1,12,11,10,7,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => [4,5,8,9,10,12,1,2,3,6,7,11] => [9,8,5,4,3,1,12,11,10,7,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => [4,5,8,9,11,12,1,2,3,6,7,10] => [9,8,5,4,2,1,12,11,10,7,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => [4,5,8,10,11,12,1,2,3,6,7,9] => [9,8,5,3,2,1,12,11,10,7,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => [4,5,9,10,11,12,1,2,3,6,7,8] => [9,8,4,3,2,1,12,11,10,7,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => [4,6,7,8,10,12,1,2,3,5,9,11] => [9,7,6,5,3,1,12,11,10,8,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => [4,6,7,8,11,12,1,2,3,5,9,10] => [9,7,6,5,2,1,12,11,10,8,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => [4,6,7,9,10,12,1,2,3,5,8,11] => [9,7,6,4,3,1,12,11,10,8,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => [4,6,7,9,11,12,1,2,3,5,8,10] => [9,7,6,4,2,1,12,11,10,8,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => [4,6,7,10,11,12,1,2,3,5,8,9] => [9,7,6,3,2,1,12,11,10,8,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => [4,6,8,9,10,12,1,2,3,5,7,11] => [9,7,5,4,3,1,12,11,10,8,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => [4,6,8,9,11,12,1,2,3,5,7,10] => [9,7,5,4,2,1,12,11,10,8,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => [4,6,8,10,11,12,1,2,3,5,7,9] => [9,7,5,3,2,1,12,11,10,8,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => [4,6,9,10,11,12,1,2,3,5,7,8] => [9,7,4,3,2,1,12,11,10,8,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => [4,7,8,9,10,12,1,2,3,5,6,11] => [9,6,5,4,3,1,12,11,10,8,7,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => [4,7,8,9,11,12,1,2,3,5,6,10] => [9,6,5,4,2,1,12,11,10,8,7,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => [4,7,8,10,11,12,1,2,3,5,6,9] => [9,6,5,3,2,1,12,11,10,8,7,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => [4,7,9,10,11,12,1,2,3,5,6,8] => [9,6,4,3,2,1,12,11,10,8,7,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => [4,8,9,10,11,12,1,2,3,5,6,7] => [9,5,4,3,2,1,12,11,10,8,7,6] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => [5,6,7,8,10,12,1,2,3,4,9,11] => [8,7,6,5,3,1,12,11,10,9,4,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => [5,6,7,8,11,12,1,2,3,4,9,10] => [8,7,6,5,2,1,12,11,10,9,4,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => [5,6,7,9,10,12,1,2,3,4,8,11] => [8,7,6,4,3,1,12,11,10,9,5,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => [5,6,7,9,11,12,1,2,3,4,8,10] => [8,7,6,4,2,1,12,11,10,9,5,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => [5,6,7,10,11,12,1,2,3,4,8,9] => [8,7,6,3,2,1,12,11,10,9,5,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => [5,6,8,9,10,12,1,2,3,4,7,11] => [8,7,5,4,3,1,12,11,10,9,6,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => [5,6,8,9,11,12,1,2,3,4,7,10] => [8,7,5,4,2,1,12,11,10,9,6,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => [5,6,8,10,11,12,1,2,3,4,7,9] => [8,7,5,3,2,1,12,11,10,9,6,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => [5,6,9,10,11,12,1,2,3,4,7,8] => [8,7,4,3,2,1,12,11,10,9,6,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => [5,7,8,9,10,12,1,2,3,4,6,11] => [8,6,5,4,3,1,12,11,10,9,7,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => [5,7,8,9,11,12,1,2,3,4,6,10] => [8,6,5,4,2,1,12,11,10,9,7,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => [5,7,8,10,11,12,1,2,3,4,6,9] => [8,6,5,3,2,1,12,11,10,9,7,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => [5,7,9,10,11,12,1,2,3,4,6,8] => [8,6,4,3,2,1,12,11,10,9,7,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => [5,8,9,10,11,12,1,2,3,4,6,7] => [8,5,4,3,2,1,12,11,10,9,7,6] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => [6,7,8,9,10,12,1,2,3,4,5,11] => [7,6,5,4,3,1,12,11,10,9,8,2] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => [6,7,8,9,11,12,1,2,3,4,5,10] => [7,6,5,4,2,1,12,11,10,9,8,3] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => [6,7,8,10,11,12,1,2,3,4,5,9] => [7,6,5,3,2,1,12,11,10,9,8,4] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => [6,7,9,10,11,12,1,2,3,4,5,8] => [7,6,4,3,2,1,12,11,10,9,8,5] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => [6,8,9,10,11,12,1,2,3,4,5,7] => [7,5,4,3,2,1,12,11,10,9,8,6] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [7,8,9,10,11,12,1,2,3,4,5,6] => [6,5,4,3,2,1,12,11,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
Map
to two-row standard tableau
Description
Return a standard tableau of shape (n,n) where n is the semilength of the Dyck path.
Given a Dyck path D, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second 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
complement
Description
Sents a permutation to its complement.
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
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.