- FindStat

Identifier

Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words

Images

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

[1,0,1,0] => [[1,3],[2,4]] => [[1,2],[3,4]] => [3,4,1,2] => 010

[1,1,0,0] => [[1,2],[3,4]] => [[1,3],[2,4]] => [2,4,1,3] => 010

[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 01010

[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 01010

[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 01010

[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 01010

[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 01010

[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 0101010

[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [[1,2],[3,4],[5,7],[6,8]] => [6,8,5,7,3,4,1,2] => 0101010

[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [[1,2],[3,5],[4,6],[7,8]] => [7,8,4,6,3,5,1,2] => 0101010

[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => 0101010

[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => 0101010

[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [[1,3],[2,4],[5,6],[7,8]] => [7,8,5,6,2,4,1,3] => 0101010

[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => 0101010

[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [[1,3],[2,5],[4,6],[7,8]] => [7,8,4,6,2,5,1,3] => 0101010

[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => 0101010

[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => 0101010

[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => 0101010

[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => 0101010

[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => 0101010

[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => 0101010

[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => 010101010

[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => [[1,2],[3,4],[5,6],[7,9],[8,10]] => [8,10,7,9,5,6,3,4,1,2] => 010101010

[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => [[1,2],[3,4],[5,7],[6,8],[9,10]] => [9,10,6,8,5,7,3,4,1,2] => 010101010

[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => [[1,2],[3,4],[5,7],[6,9],[8,10]] => [8,10,6,9,5,7,3,4,1,2] => 010101010

[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => [[1,2],[3,4],[5,8],[6,9],[7,10]] => [7,10,6,9,5,8,3,4,1,2] => 010101010

[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => [[1,2],[3,5],[4,6],[7,8],[9,10]] => [9,10,7,8,4,6,3,5,1,2] => 010101010

[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => [[1,2],[3,5],[4,6],[7,9],[8,10]] => [8,10,7,9,4,6,3,5,1,2] => 010101010

[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => [[1,2],[3,5],[4,7],[6,8],[9,10]] => [9,10,6,8,4,7,3,5,1,2] => 010101010

[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => [[1,2],[3,5],[4,7],[6,9],[8,10]] => [8,10,6,9,4,7,3,5,1,2] => 010101010

[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => [[1,2],[3,5],[4,8],[6,9],[7,10]] => [7,10,6,9,4,8,3,5,1,2] => 010101010

[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => [[1,2],[3,6],[4,7],[5,8],[9,10]] => [9,10,5,8,4,7,3,6,1,2] => 010101010

[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => [[1,2],[3,6],[4,7],[5,9],[8,10]] => [8,10,5,9,4,7,3,6,1,2] => 010101010

[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => [[1,2],[3,6],[4,8],[5,9],[7,10]] => [7,10,5,9,4,8,3,6,1,2] => 010101010

[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => [[1,2],[3,7],[4,8],[5,9],[6,10]] => [6,10,5,9,4,8,3,7,1,2] => 010101010

[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => [[1,3],[2,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,2,4,1,3] => 010101010

[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => [[1,3],[2,4],[5,6],[7,9],[8,10]] => [8,10,7,9,5,6,2,4,1,3] => 010101010

[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => [[1,3],[2,4],[5,7],[6,8],[9,10]] => [9,10,6,8,5,7,2,4,1,3] => 010101010

[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => [[1,3],[2,4],[5,7],[6,9],[8,10]] => [8,10,6,9,5,7,2,4,1,3] => 010101010

[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => [[1,3],[2,4],[5,8],[6,9],[7,10]] => [7,10,6,9,5,8,2,4,1,3] => 010101010

[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => [[1,3],[2,5],[4,6],[7,8],[9,10]] => [9,10,7,8,4,6,2,5,1,3] => 010101010

[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => [[1,3],[2,5],[4,6],[7,9],[8,10]] => [8,10,7,9,4,6,2,5,1,3] => 010101010

[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => [[1,3],[2,5],[4,7],[6,8],[9,10]] => [9,10,6,8,4,7,2,5,1,3] => 010101010

[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => [[1,3],[2,5],[4,7],[6,9],[8,10]] => [8,10,6,9,4,7,2,5,1,3] => 010101010

[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => [[1,3],[2,5],[4,8],[6,9],[7,10]] => [7,10,6,9,4,8,2,5,1,3] => 010101010

[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => [[1,3],[2,6],[4,7],[5,8],[9,10]] => [9,10,5,8,4,7,2,6,1,3] => 010101010

[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => [[1,3],[2,6],[4,7],[5,9],[8,10]] => [8,10,5,9,4,7,2,6,1,3] => 010101010

[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => [[1,3],[2,6],[4,8],[5,9],[7,10]] => [7,10,5,9,4,8,2,6,1,3] => 010101010

[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => [[1,3],[2,7],[4,8],[5,9],[6,10]] => [6,10,5,9,4,8,2,7,1,3] => 010101010

[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => [[1,4],[2,5],[3,6],[7,8],[9,10]] => [9,10,7,8,3,6,2,5,1,4] => 010101010

[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => [[1,4],[2,5],[3,6],[7,9],[8,10]] => [8,10,7,9,3,6,2,5,1,4] => 010101010

[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => [[1,4],[2,5],[3,7],[6,8],[9,10]] => [9,10,6,8,3,7,2,5,1,4] => 010101010

[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => [[1,4],[2,5],[3,7],[6,9],[8,10]] => [8,10,6,9,3,7,2,5,1,4] => 010101010

[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => [[1,4],[2,5],[3,8],[6,9],[7,10]] => [7,10,6,9,3,8,2,5,1,4] => 010101010

[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => [[1,4],[2,6],[3,7],[5,8],[9,10]] => [9,10,5,8,3,7,2,6,1,4] => 010101010

[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => [[1,4],[2,6],[3,7],[5,9],[8,10]] => [8,10,5,9,3,7,2,6,1,4] => 010101010

[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => [[1,4],[2,6],[3,8],[5,9],[7,10]] => [7,10,5,9,3,8,2,6,1,4] => 010101010

[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => [[1,4],[2,7],[3,8],[5,9],[6,10]] => [6,10,5,9,3,8,2,7,1,4] => 010101010

[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => [[1,5],[2,6],[3,7],[4,8],[9,10]] => [9,10,4,8,3,7,2,6,1,5] => 010101010

[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => [[1,5],[2,6],[3,7],[4,9],[8,10]] => [8,10,4,9,3,7,2,6,1,5] => 010101010

[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => [[1,5],[2,6],[3,8],[4,9],[7,10]] => [7,10,4,9,3,8,2,6,1,5] => 010101010

[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => [[1,5],[2,7],[3,8],[4,9],[6,10]] => [6,10,4,9,3,8,2,7,1,5] => 010101010

[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => [5,10,4,9,3,8,2,7,1,6] => 010101010

[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,5,6,3,4,1,2] => 01010101010

[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => [[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,5,6,3,4,1,2] => 01010101010

[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => [[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,5,6,3,4,1,2] => 01010101010

[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => [[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,5,6,3,4,1,2] => 01010101010

[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => [[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,5,6,3,4,1,2] => 01010101010

[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => [[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,5,7,3,4,1,2] => 01010101010

[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => [[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,5,7,3,4,1,2] => 01010101010

[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => [[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,5,7,3,4,1,2] => 01010101010

[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => [[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,5,7,3,4,1,2] => 01010101010

[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => [[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,5,7,3,4,1,2] => 01010101010

[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => [[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,5,8,3,4,1,2] => 01010101010

[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => [[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,5,8,3,4,1,2] => 01010101010

[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => [[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,5,8,3,4,1,2] => 01010101010

[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => [[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,5,9,3,4,1,2] => 01010101010

[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => [[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,4,6,3,5,1,2] => 01010101010

[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => [[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,4,6,3,5,1,2] => 01010101010

[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => [[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,4,6,3,5,1,2] => 01010101010

[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => [[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,4,6,3,5,1,2] => 01010101010

[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => [[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,4,6,3,5,1,2] => 01010101010

[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => [[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,4,7,3,5,1,2] => 01010101010

[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => [[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,4,7,3,5,1,2] => 01010101010

[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => [[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,4,7,3,5,1,2] => 01010101010

[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => [[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,4,7,3,5,1,2] => 01010101010

[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => [[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,4,7,3,5,1,2] => 01010101010

[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => [[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,4,8,3,5,1,2] => 01010101010

[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => [[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,4,8,3,5,1,2] => 01010101010

[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => [[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,4,8,3,5,1,2] => 01010101010

[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => [[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,4,9,3,5,1,2] => 01010101010

[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => [[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]] => [11,12,9,10,5,8,4,7,3,6,1,2] => 01010101010

[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => [[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]] => [10,12,9,11,5,8,4,7,3,6,1,2] => 01010101010

[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => [[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]] => [11,12,8,10,5,9,4,7,3,6,1,2] => 01010101010

[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => [[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]] => [10,12,8,11,5,9,4,7,3,6,1,2] => 01010101010

[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => [[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]] => [9,12,8,11,5,10,4,7,3,6,1,2] => 01010101010

[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => [[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]] => [11,12,7,10,5,9,4,8,3,6,1,2] => 01010101010

[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => [[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]] => [10,12,7,11,5,9,4,8,3,6,1,2] => 01010101010

[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => [[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]] => [9,12,7,11,5,10,4,8,3,6,1,2] => 01010101010

[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => [[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]] => [8,12,7,11,5,10,4,9,3,6,1,2] => 01010101010

>>> 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]] => [[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]] => [11,12,6,10,5,9,4,8,3,7,1,2] => 01010101010

[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => [[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]] => [10,12,6,11,5,9,4,8,3,7,1,2] => 01010101010

[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => [[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]] => [9,12,6,11,5,10,4,8,3,7,1,2] => 01010101010

[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => [[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]] => [8,12,6,11,5,10,4,9,3,7,1,2] => 01010101010

[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => [[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]] => [7,12,6,11,5,10,4,9,3,8,1,2] => 01010101010

[1,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => [[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,5,6,2,4,1,3] => 01010101010

[1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => [[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,5,6,2,4,1,3] => 01010101010

[1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => [[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,5,6,2,4,1,3] => 01010101010

[1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => [[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,5,6,2,4,1,3] => 01010101010

[1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => [[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,5,6,2,4,1,3] => 01010101010

[1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => [[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,5,7,2,4,1,3] => 01010101010

[1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => [[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,5,7,2,4,1,3] => 01010101010

[1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => [[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,5,7,2,4,1,3] => 01010101010

[1,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => [[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,5,7,2,4,1,3] => 01010101010

[1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => [[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,5,7,2,4,1,3] => 01010101010

[1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => [[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,5,8,2,4,1,3] => 01010101010

[1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => [[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,5,8,2,4,1,3] => 01010101010

[1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => [[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,5,8,2,4,1,3] => 01010101010

[1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => [[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,5,9,2,4,1,3] => 01010101010

[1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => [[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,4,6,2,5,1,3] => 01010101010

[1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => [[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,4,6,2,5,1,3] => 01010101010

[1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => [[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,4,6,2,5,1,3] => 01010101010

[1,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => [[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,4,6,2,5,1,3] => 01010101010

[1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => [[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,4,6,2,5,1,3] => 01010101010

[1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => [[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,4,7,2,5,1,3] => 01010101010

[1,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => [[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,4,7,2,5,1,3] => 01010101010

[1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => [[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,4,7,2,5,1,3] => 01010101010

[1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => [[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,4,7,2,5,1,3] => 01010101010

[1,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => [[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,4,7,2,5,1,3] => 01010101010

[1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => [[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,4,8,2,5,1,3] => 01010101010

[1,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => [[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,4,8,2,5,1,3] => 01010101010

[1,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => [[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,4,8,2,5,1,3] => 01010101010

[1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => [[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,4,9,2,5,1,3] => 01010101010

[1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => [[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]] => [11,12,9,10,5,8,4,7,2,6,1,3] => 01010101010

[1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => [[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]] => [10,12,9,11,5,8,4,7,2,6,1,3] => 01010101010

[1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => [[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]] => [11,12,8,10,5,9,4,7,2,6,1,3] => 01010101010

[1,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => [[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]] => [10,12,8,11,5,9,4,7,2,6,1,3] => 01010101010

[1,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => [[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]] => [9,12,8,11,5,10,4,7,2,6,1,3] => 01010101010

[1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => [[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]] => [11,12,7,10,5,9,4,8,2,6,1,3] => 01010101010

[1,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => [[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]] => [10,12,7,11,5,9,4,8,2,6,1,3] => 01010101010

[1,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => [[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]] => [9,12,7,11,5,10,4,8,2,6,1,3] => 01010101010

[1,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => [[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]] => [8,12,7,11,5,10,4,9,2,6,1,3] => 01010101010

[1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => [[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]] => [11,12,6,10,5,9,4,8,2,7,1,3] => 01010101010

[1,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => [[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]] => [10,12,6,11,5,9,4,8,2,7,1,3] => 01010101010

[1,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => [[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]] => [9,12,6,11,5,10,4,8,2,7,1,3] => 01010101010

[1,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => [[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]] => [8,12,6,11,5,10,4,9,2,7,1,3] => 01010101010

[1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => [[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]] => [7,12,6,11,5,10,4,9,2,8,1,3] => 01010101010

[1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => [[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,3,6,2,5,1,4] => 01010101010

[1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => [[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,3,6,2,5,1,4] => 01010101010

[1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => [[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,3,6,2,5,1,4] => 01010101010

[1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => [[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,3,6,2,5,1,4] => 01010101010

[1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => [[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,3,6,2,5,1,4] => 01010101010

[1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => [[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,3,7,2,5,1,4] => 01010101010

[1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => [[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,3,7,2,5,1,4] => 01010101010

[1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => [[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,3,7,2,5,1,4] => 01010101010

[1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => [[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,3,7,2,5,1,4] => 01010101010

[1,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => [[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,3,7,2,5,1,4] => 01010101010

[1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => [[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,3,8,2,5,1,4] => 01010101010

[1,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => [[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,3,8,2,5,1,4] => 01010101010

[1,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => [[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,3,8,2,5,1,4] => 01010101010

[1,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => [[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,3,9,2,5,1,4] => 01010101010

[1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => [[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]] => [11,12,9,10,5,8,3,7,2,6,1,4] => 01010101010

[1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => [[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]] => [10,12,9,11,5,8,3,7,2,6,1,4] => 01010101010

[1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => [[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]] => [11,12,8,10,5,9,3,7,2,6,1,4] => 01010101010

[1,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => [[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]] => [10,12,8,11,5,9,3,7,2,6,1,4] => 01010101010

[1,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => [[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]] => [9,12,8,11,5,10,3,7,2,6,1,4] => 01010101010

[1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => [[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]] => [11,12,7,10,5,9,3,8,2,6,1,4] => 01010101010

[1,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => [[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]] => [10,12,7,11,5,9,3,8,2,6,1,4] => 01010101010

[1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => [[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]] => [9,12,7,11,5,10,3,8,2,6,1,4] => 01010101010

[1,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => [[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]] => [8,12,7,11,5,10,3,9,2,6,1,4] => 01010101010

[1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => [[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]] => [11,12,6,10,5,9,3,8,2,7,1,4] => 01010101010

[1,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => [[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]] => [10,12,6,11,5,9,3,8,2,7,1,4] => 01010101010

[1,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => [[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]] => [9,12,6,11,5,10,3,8,2,7,1,4] => 01010101010

[1,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => [[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]] => [8,12,6,11,5,10,3,9,2,7,1,4] => 01010101010

[1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => [[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]] => [7,12,6,11,5,10,3,9,2,8,1,4] => 01010101010

[1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => [[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]] => [11,12,9,10,4,8,3,7,2,6,1,5] => 01010101010

[1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => [[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]] => [10,12,9,11,4,8,3,7,2,6,1,5] => 01010101010

[1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => [[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]] => [11,12,8,10,4,9,3,7,2,6,1,5] => 01010101010

[1,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => [[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]] => [10,12,8,11,4,9,3,7,2,6,1,5] => 01010101010

[1,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => [[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]] => [9,12,8,11,4,10,3,7,2,6,1,5] => 01010101010

[1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => [[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]] => [11,12,7,10,4,9,3,8,2,6,1,5] => 01010101010

[1,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => [[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]] => [10,12,7,11,4,9,3,8,2,6,1,5] => 01010101010

[1,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => [[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]] => [9,12,7,11,4,10,3,8,2,6,1,5] => 01010101010

[1,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => [[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]] => [8,12,7,11,4,10,3,9,2,6,1,5] => 01010101010

[1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => [[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]] => [11,12,6,10,4,9,3,8,2,7,1,5] => 01010101010

[1,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => [[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]] => [10,12,6,11,4,9,3,8,2,7,1,5] => 01010101010

[1,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => [[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]] => [9,12,6,11,4,10,3,8,2,7,1,5] => 01010101010

[1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => [[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]] => [8,12,6,11,4,10,3,9,2,7,1,5] => 01010101010

[1,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => [[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]] => [7,12,6,11,4,10,3,9,2,8,1,5] => 01010101010

[1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => [[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]] => [11,12,5,10,4,9,3,8,2,7,1,6] => 01010101010

[1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => [[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]] => [10,12,5,11,4,9,3,8,2,7,1,6] => 01010101010

[1,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => [[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]] => [9,12,5,11,4,10,3,8,2,7,1,6] => 01010101010

[1,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => [[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]] => [8,12,5,11,4,10,3,9,2,7,1,6] => 01010101010

[1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => [[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]] => [7,12,5,11,4,10,3,9,2,8,1,6] => 01010101010

[1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => [6,12,5,11,4,10,3,9,2,8,1,7] => 01010101010

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

conjugate

Description

Sends a standard tableau to its conjugate tableau.

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

descent word

Description

The descent positions of a permutation as a binary word.
For a permutation

$\pi$ of

$n$ letters and each

$1\leq i\leq n-1$ such that

$\pi(i) > \pi(i+1)$ we set

$w_i=1$ , otherwise

$w_i=0$ .
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.