Identifier
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Images
[1,0] => [[1],[2]] => [2,1] => [2,1] => [1,2]
[1,0,1,0] => [[1,3],[2,4]] => [2,4,1,3] => [2,1,4,3] => [1,2,3,4]
[1,1,0,0] => [[1,2],[3,4]] => [3,4,1,2] => [1,3,4,2] => [1,2,3,4]
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [2,1,4,3,6,5] => [1,2,3,4,5,6]
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [2,1,3,5,6,4] => [1,2,3,4,5,6]
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [1,3,4,2,6,5] => [1,2,3,4,5,6]
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [1,3,2,5,6,4] => [1,2,3,4,5,6]
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [1,2,4,5,6,3] => [1,2,3,4,5,6]
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => [2,1,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8]
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => [2,1,4,3,5,7,8,6] => [1,2,3,4,5,6,7,8]
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [2,5,6,8,1,3,4,7] => [2,1,3,5,6,4,8,7] => [1,2,3,4,5,6,7,8]
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [2,5,7,8,1,3,4,6] => [2,1,3,5,4,7,8,6] => [1,2,3,4,5,6,7,8]
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [2,6,7,8,1,3,4,5] => [2,1,3,4,6,7,8,5] => [1,2,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => [1,3,4,2,6,5,8,7] => [1,2,3,4,5,6,7,8]
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [3,4,7,8,1,2,5,6] => [1,3,4,2,5,7,8,6] => [1,2,3,4,5,6,7,8]
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => [1,3,2,5,6,4,8,7] => [1,2,3,4,5,6,7,8]
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => [1,3,2,5,4,7,8,6] => [1,2,3,4,5,6,7,8]
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => [1,3,2,4,6,7,8,5] => [1,2,3,4,5,6,7,8]
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => [1,2,4,5,6,3,8,7] => [1,2,3,4,5,6,7,8]
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [1,2,4,5,3,7,8,6] => [1,2,3,4,5,6,7,8]
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [4,6,7,8,1,2,3,5] => [1,2,4,3,6,7,8,5] => [1,2,3,4,5,6,7,8]
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [1,2,3,5,6,7,8,4] => [1,2,3,4,5,6,7,8]
[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] => [2,1,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,4,3,6,5,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,4,3,5,7,8,6,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,4,3,5,7,6,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,4,3,5,6,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,5,6,4,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,5,6,4,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,5,4,7,8,6,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,5,4,7,6,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,5,4,6,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,4,6,7,8,5,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,4,6,7,5,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,4,6,5,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,3,4,5,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,4,2,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,4,2,6,5,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,4,2,5,7,8,6,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,4,2,5,7,6,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,4,2,5,6,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,5,6,4,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,5,6,4,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,5,4,7,8,6,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,5,4,7,6,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,5,4,6,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,4,6,7,8,5,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,4,6,7,5,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,4,6,5,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,3,2,4,5,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,5,6,3,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,5,6,3,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,5,3,7,8,6,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,5,3,7,6,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,5,3,6,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,3,6,7,8,5,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,3,6,7,5,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,3,6,5,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,4,3,5,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,3,5,6,7,8,4,10,9] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,3,5,6,7,4,9,10,8] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,3,5,6,4,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,3,5,4,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10]
[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] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,5,6,7,8,9,10]
[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] => [2,1,4,3,6,5,8,7,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,6,5,8,7,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,6,5,7,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,6,5,7,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,6,5,7,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,7,8,6,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,7,8,6,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,7,6,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,7,6,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,7,6,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,6,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,6,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,6,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,4,3,5,6,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,6,4,8,7,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,6,4,8,7,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,6,4,7,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,6,4,7,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,6,4,7,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,7,8,6,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,7,8,6,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,7,6,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,7,6,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,7,6,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,6,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,6,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,6,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,5,4,6,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,7,8,5,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,7,8,5,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,7,5,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,7,5,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,7,5,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,5,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,5,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,5,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,6,5,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
>>> 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] => [2,1,3,4,5,7,8,9,10,6,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,5,7,8,9,6,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,5,7,8,6,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,5,7,6,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [2,1,3,4,5,6,8,9,10,11,12,7] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,6,5,8,7,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,6,5,8,7,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,6,5,7,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,6,5,7,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,6,5,7,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,7,8,6,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,7,8,6,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,7,6,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,7,6,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,7,6,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,6,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,6,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,6,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,4,2,5,6,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,6,4,8,7,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,6,4,8,7,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,6,4,7,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,6,4,7,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,6,4,7,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,7,8,6,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,7,8,6,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,7,6,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,7,6,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,7,6,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,6,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,6,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,6,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,5,4,6,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,7,8,5,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,7,8,5,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,7,5,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,7,5,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,7,5,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,5,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,5,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,5,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,6,5,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,5,7,8,9,10,6,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,5,7,8,9,6,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,5,7,8,6,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,5,7,6,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,3,2,4,5,6,8,9,10,11,12,7] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,6,3,8,7,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,6,3,8,7,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,6,3,7,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,6,3,7,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,6,3,7,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,7,8,6,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,7,8,6,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,7,6,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,7,6,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,7,6,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,6,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,6,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,6,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,5,3,6,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,7,8,5,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,7,8,5,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,7,5,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,7,5,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,7,5,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,5,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,5,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,5,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,6,5,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,5,7,8,9,10,6,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,5,7,8,9,6,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,5,7,8,6,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,5,7,6,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,4,3,5,6,8,9,10,11,12,7] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,7,8,4,10,9,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,7,8,4,9,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,7,4,9,10,8,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,7,4,9,8,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,7,4,8,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,4,8,9,10,7,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,4,8,9,7,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,4,8,7,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,6,4,7,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,4,7,8,9,10,6,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,4,7,8,9,6,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,4,7,8,6,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,4,7,6,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,5,4,6,8,9,10,11,12,7] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,4,6,7,8,9,10,5,12,11] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,4,6,7,8,9,5,11,12,10] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,4,6,7,8,5,10,11,12,9] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,4,6,7,5,9,10,11,12,8] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,4,6,5,8,9,10,11,12,7] => [1,2,3,4,5,6,7,8,9,10,11,12]
[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] => [1,2,3,4,5,7,8,9,10,11,12,6] => [1,2,3,4,5,6,7,8,9,10,11,12]
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
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.