- FindStat

Identifier

Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux

Images

[1,0] => [[1],[2]] => [2,1] => [1,2] => [[1,2]]

[1,0,1,0] => [[1,3],[2,4]] => [2,4,1,3] => [3,1,4,2] => [[1,3],[2,4]]

[1,1,0,0] => [[1,2],[3,4]] => [3,4,1,2] => [2,1,4,3] => [[1,3],[2,4]]

[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => [[1,4],[2,5],[3,6]]

[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [[1,4],[2,5],[3,6]]

[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [[1,4],[2,5],[3,6]]

[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [[1,4],[2,5],[3,6]]

[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]]

[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] => [[1,5],[2,6],[3,7],[4,8]]

[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => [6,5,3,1,8,7,4,2] => [[1,5],[2,6],[3,7],[4,8]]

[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] => [[1,5],[2,6],[3,7],[4,8]]

[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [2,5,7,8,1,3,4,6] => [6,4,3,1,8,7,5,2] => [[1,5],[2,6],[3,7],[4,8]]

[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [2,6,7,8,1,3,4,5] => [5,4,3,1,8,7,6,2] => [[1,5],[2,6],[3,7],[4,8]]

[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => [7,5,2,1,8,6,4,3] => [[1,5],[2,6],[3,7],[4,8]]

[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] => [[1,5],[2,6],[3,7],[4,8]]

[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => [7,4,2,1,8,6,5,3] => [[1,5],[2,6],[3,7],[4,8]]

[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] => [[1,5],[2,6],[3,7],[4,8]]

[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => [5,4,2,1,8,7,6,3] => [[1,5],[2,6],[3,7],[4,8]]

[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => [7,3,2,1,8,6,5,4] => [[1,5],[2,6],[3,7],[4,8]]

[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [6,3,2,1,8,7,5,4] => [[1,5],[2,6],[3,7],[4,8]]

[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] => [[1,5],[2,6],[3,7],[4,8]]

[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] => [[1,5],[2,6],[3,7],[4,8]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,7,5,3,1,10,9,6,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,6,5,3,1,10,8,7,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,6,5,3,1,10,9,7,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [7,6,5,3,1,10,9,8,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,7,4,3,1,10,8,6,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,7,4,3,1,10,9,6,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,6,4,3,1,10,9,7,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [7,6,4,3,1,10,9,8,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,5,4,3,1,10,9,7,6,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [7,5,4,3,1,10,9,8,6,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [6,5,4,3,1,10,9,8,7,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,7,5,2,1,10,8,6,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,6,5,2,1,10,8,7,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,6,5,2,1,10,9,7,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [7,6,5,2,1,10,9,8,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,7,4,2,1,10,8,6,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,7,4,2,1,10,9,6,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,6,4,2,1,10,8,7,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [7,6,4,2,1,10,9,8,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,5,4,2,1,10,8,7,6,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [7,5,4,2,1,10,9,8,6,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [6,5,4,2,1,10,9,8,7,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,7,3,2,1,10,8,6,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,7,3,2,1,10,9,6,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,6,3,2,1,10,8,7,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,6,3,2,1,10,9,7,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,5,3,2,1,10,8,7,6,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,5,3,2,1,10,9,7,6,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [6,5,3,2,1,10,9,8,7,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [9,4,3,2,1,10,8,7,6,5] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [8,4,3,2,1,10,9,7,6,5] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [7,4,3,2,1,10,9,8,6,5] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,6],[2,7],[3,8],[4,9],[5,10]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,7,5,3,1,12,11,8,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,7,5,3,1,12,10,9,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,7,5,3,1,12,11,9,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,7,5,3,1,12,11,10,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,6,5,3,1,12,11,8,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,6,5,3,1,12,10,9,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,6,5,3,1,12,11,9,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,6,5,3,1,12,11,10,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,7,6,5,3,1,12,10,9,8,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,7,6,5,3,1,12,11,9,8,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,7,6,5,3,1,12,11,10,8,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,7,6,5,3,1,12,11,10,9,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,7,4,3,1,12,10,8,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,7,4,3,1,12,11,8,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,7,4,3,1,12,11,9,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,7,4,3,1,12,11,10,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,6,4,3,1,12,10,8,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,6,4,3,1,12,11,8,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,6,4,3,1,12,11,9,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,6,4,3,1,12,11,10,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,7,6,4,3,1,12,10,9,8,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,7,6,4,3,1,12,11,9,8,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,7,6,4,3,1,12,11,10,8,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,7,6,4,3,1,12,11,10,9,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,5,4,3,1,12,10,8,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,5,4,3,1,12,11,8,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,5,4,3,1,12,10,9,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,5,4,3,1,12,11,9,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,5,4,3,1,12,11,10,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,7,5,4,3,1,12,11,9,8,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,7,5,4,3,1,12,11,10,8,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,7,5,4,3,1,12,11,10,9,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

>>> 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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,6,5,4,3,1,12,11,9,8,7,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,6,5,4,3,1,12,11,10,8,7,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,6,5,4,3,1,12,11,10,9,7,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [7,6,5,4,3,1,12,11,10,9,8,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,7,5,2,1,12,10,8,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,7,5,2,1,12,10,9,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,7,5,2,1,12,11,9,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,7,5,2,1,12,11,10,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,6,5,2,1,12,10,8,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,6,5,2,1,12,10,9,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,6,5,2,1,12,11,9,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,6,5,2,1,12,11,10,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,7,6,5,2,1,12,10,9,8,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,7,6,5,2,1,12,11,9,8,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,7,6,5,2,1,12,11,10,8,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,7,6,5,2,1,12,11,10,9,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,7,4,2,1,12,10,8,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,7,4,2,1,12,11,8,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,7,4,2,1,12,10,9,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,7,4,2,1,12,11,10,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,6,4,2,1,12,10,8,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,6,4,2,1,12,11,8,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,6,4,2,1,12,10,9,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,6,4,2,1,12,11,10,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,7,6,4,2,1,12,10,9,8,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,7,6,4,2,1,12,11,9,8,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,7,6,4,2,1,12,11,10,8,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,7,6,4,2,1,12,11,10,9,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,5,4,2,1,12,10,8,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,5,4,2,1,12,11,8,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,5,4,2,1,12,10,9,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,5,4,2,1,12,11,9,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,5,4,2,1,12,11,10,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,7,5,4,2,1,12,10,9,8,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,7,5,4,2,1,12,11,10,8,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,7,5,4,2,1,12,11,10,9,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,6,5,4,2,1,12,10,9,8,7,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,6,5,4,2,1,12,11,10,8,7,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,6,5,4,2,1,12,11,10,9,7,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [7,6,5,4,2,1,12,11,10,9,8,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,7,3,2,1,12,10,8,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,7,3,2,1,12,11,8,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,7,3,2,1,12,10,9,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,7,3,2,1,12,11,9,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,6,3,2,1,12,10,8,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,6,3,2,1,12,11,8,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,6,3,2,1,12,10,9,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,6,3,2,1,12,11,9,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,7,6,3,2,1,12,10,9,8,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,7,6,3,2,1,12,11,9,8,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,7,6,3,2,1,12,11,10,8,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,7,6,3,2,1,12,11,10,9,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,5,3,2,1,12,10,8,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,5,3,2,1,12,11,8,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,5,3,2,1,12,10,9,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,5,3,2,1,12,11,9,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,5,3,2,1,12,11,10,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,7,5,3,2,1,12,10,9,8,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,7,5,3,2,1,12,11,9,8,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,7,5,3,2,1,12,11,10,9,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,6,5,3,2,1,12,10,9,8,7,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,6,5,3,2,1,12,11,9,8,7,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,6,5,3,2,1,12,11,10,9,7,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [7,6,5,3,2,1,12,11,10,9,8,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,9,4,3,2,1,12,10,8,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,9,4,3,2,1,12,11,8,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,8,4,3,2,1,12,10,9,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,8,4,3,2,1,12,11,9,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,8,4,3,2,1,12,11,10,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,7,4,3,2,1,12,10,9,8,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,7,4,3,2,1,12,11,9,8,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,7,4,3,2,1,12,11,10,8,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,6,4,3,2,1,12,10,9,8,7,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,6,4,3,2,1,12,11,9,8,7,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,6,4,3,2,1,12,11,10,8,7,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [7,6,4,3,2,1,12,11,10,9,8,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [11,5,4,3,2,1,12,10,9,8,7,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [10,5,4,3,2,1,12,11,9,8,7,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [9,5,4,3,2,1,12,11,10,8,7,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [8,5,4,3,2,1,12,11,10,9,7,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

[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] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]

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

reverse

Description

Sends a permutation to its reverse.
The reverse of a permutation

$\sigma$ of length

$n$ is given by

$\tau$ with

$\tau(i) = \sigma(n+1-i)$ .

Map

Robinson-Schensted recording tableau

Description

Sends a permutation to its Robinson-Schensted recording tableau.
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 its corresponding recording tableau.