Identifier
Mp00033:
Dyck paths
—to two-row standard tableau⟶
Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Images
[1,0] => [[1],[2]] => [[1,2]] => [1,2] => [1,1]
[1,0,1,0] => [[1,3],[2,4]] => [[1,2],[3,4]] => [3,4,1,2] => [2,1,1]
[1,1,0,0] => [[1,2],[3,4]] => [[1,3],[2,4]] => [2,4,1,3] => [2,1,1]
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [3,1,1,1]
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [3,1,1,1]
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [3,1,1,1]
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [3,1,1,1]
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [3,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [4,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [5,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
[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] => [6,1,1,1,1,1,1]
>>> Load all 196 entries. <<<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.
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
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
searching the database
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