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Identifier
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Images
[1,0] => [[1],[2]] => [2,1] => [2,1]
[1,0,1,0] => [[1,3],[2,4]] => [2,4,1,3] => [4,2,1,3]
[1,1,0,0] => [[1,2],[3,4]] => [3,4,1,2] => [4,1,3,2]
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [6,2,1,4,3,5]
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [6,2,1,3,5,4]
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [6,1,3,4,2,5]
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [6,1,3,2,5,4]
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [6,1,2,4,5,3]
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => [8,2,1,4,3,6,5,7]
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => [8,2,1,4,3,5,7,6]
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [2,5,6,8,1,3,4,7] => [8,2,1,3,5,6,4,7]
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [2,5,7,8,1,3,4,6] => [8,2,1,3,5,4,7,6]
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [2,6,7,8,1,3,4,5] => [8,2,1,3,4,6,7,5]
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => [8,1,3,4,2,6,5,7]
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [3,4,7,8,1,2,5,6] => [8,1,3,4,2,5,7,6]
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => [8,1,3,2,5,6,4,7]
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => [8,1,3,2,5,4,7,6]
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => [8,1,3,2,4,6,7,5]
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => [8,1,2,4,5,6,3,7]
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [8,1,2,4,5,3,7,6]
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [4,6,7,8,1,2,3,5] => [8,1,2,4,3,6,7,5]
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4]
[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] => [10,2,1,4,3,6,5,8,7,9]
[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] => [10,2,1,4,3,6,5,7,9,8]
[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] => [10,2,1,4,3,5,7,8,6,9]
[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] => [10,2,1,4,3,5,7,6,9,8]
[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] => [10,2,1,4,3,5,6,8,9,7]
[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] => [10,2,1,3,5,6,4,8,7,9]
[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] => [10,2,1,3,5,6,4,7,9,8]
[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] => [10,2,1,3,5,4,7,8,6,9]
[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] => [10,2,1,3,5,4,7,6,9,8]
[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] => [10,2,1,3,5,4,6,8,9,7]
[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] => [10,2,1,3,4,6,7,8,5,9]
[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] => [10,2,1,3,4,6,7,5,9,8]
[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] => [10,2,1,3,4,6,5,8,9,7]
[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] => [10,2,1,3,4,5,7,8,9,6]
[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] => [10,1,3,4,2,6,5,8,7,9]
[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] => [10,1,3,4,2,6,5,7,9,8]
[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] => [10,1,3,4,2,5,7,8,6,9]
[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] => [10,1,3,4,2,5,7,6,9,8]
[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] => [10,1,3,4,2,5,6,8,9,7]
[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] => [10,1,3,2,5,6,4,8,7,9]
[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] => [10,1,3,2,5,6,4,7,9,8]
[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] => [10,1,3,2,5,4,7,8,6,9]
[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] => [10,1,3,2,5,4,7,6,9,8]
[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] => [10,1,3,2,5,4,6,8,9,7]
[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] => [10,1,3,2,4,6,7,8,5,9]
[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] => [10,1,3,2,4,6,7,5,9,8]
[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] => [10,1,3,2,4,6,5,8,9,7]
[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] => [10,1,3,2,4,5,7,8,9,6]
[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] => [10,1,2,4,5,6,3,8,7,9]
[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] => [10,1,2,4,5,6,3,7,9,8]
[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] => [10,1,2,4,5,3,7,8,6,9]
[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] => [10,1,2,4,5,3,7,6,9,8]
[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] => [10,1,2,4,5,3,6,8,9,7]
[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] => [10,1,2,4,3,6,7,8,5,9]
[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] => [10,1,2,4,3,6,7,5,9,8]
[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] => [10,1,2,4,3,6,5,8,9,7]
[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] => [10,1,2,4,3,5,7,8,9,6]
[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] => [10,1,2,3,5,6,7,8,4,9]
[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] => [10,1,2,3,5,6,7,4,9,8]
[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] => [10,1,2,3,5,6,4,8,9,7]
[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] => [10,1,2,3,5,4,7,8,9,6]
[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] => [10,1,2,3,4,6,7,8,9,5]
[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] => [12,2,1,4,3,6,5,8,7,10,9,11]
[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] => [12,2,1,4,3,6,5,8,7,9,11,10]
[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] => [12,2,1,4,3,6,5,7,9,10,8,11]
[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] => [12,2,1,4,3,6,5,7,9,8,11,10]
[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] => [12,2,1,4,3,6,5,7,8,10,11,9]
[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] => [12,2,1,4,3,5,7,8,6,10,9,11]
[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] => [12,2,1,4,3,5,7,8,6,9,11,10]
[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] => [12,2,1,4,3,5,7,6,9,10,8,11]
[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] => [12,2,1,4,3,5,7,6,9,8,11,10]
[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] => [12,2,1,4,3,5,7,6,8,10,11,9]
[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] => [12,2,1,4,3,5,6,8,9,10,7,11]
[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] => [12,2,1,4,3,5,6,8,9,7,11,10]
[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] => [12,2,1,4,3,5,6,8,7,10,11,9]
[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] => [12,2,1,4,3,5,6,7,9,10,11,8]
[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] => [12,2,1,3,5,6,4,8,7,10,9,11]
[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] => [12,2,1,3,5,6,4,8,7,9,11,10]
[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] => [12,2,1,3,5,6,4,7,9,10,8,11]
[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] => [12,2,1,3,5,6,4,7,9,8,11,10]
[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] => [12,2,1,3,5,6,4,7,8,10,11,9]
[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] => [12,2,1,3,5,4,7,8,6,10,9,11]
[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] => [12,2,1,3,5,4,7,8,6,9,11,10]
[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] => [12,2,1,3,5,4,7,6,9,10,8,11]
[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] => [12,2,1,3,5,4,7,6,9,8,11,10]
[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] => [12,2,1,3,5,4,7,6,8,10,11,9]
[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] => [12,2,1,3,5,4,6,8,9,10,7,11]
[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] => [12,2,1,3,5,4,6,8,9,7,11,10]
[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] => [12,2,1,3,5,4,6,8,7,10,11,9]
[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] => [12,2,1,3,5,4,6,7,9,10,11,8]
[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] => [12,2,1,3,4,6,7,8,5,10,9,11]
[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] => [12,2,1,3,4,6,7,8,5,9,11,10]
[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] => [12,2,1,3,4,6,7,5,9,10,8,11]
[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] => [12,2,1,3,4,6,7,5,9,8,11,10]
[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] => [12,2,1,3,4,6,7,5,8,10,11,9]
[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] => [12,2,1,3,4,6,5,8,9,10,7,11]
[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] => [12,2,1,3,4,6,5,8,9,7,11,10]
[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] => [12,2,1,3,4,6,5,8,7,10,11,9]
[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] => [12,2,1,3,4,6,5,7,9,10,11,8]
>>> 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] => [12,2,1,3,4,5,7,8,9,10,6,11]
[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] => [12,2,1,3,4,5,7,8,9,6,11,10]
[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] => [12,2,1,3,4,5,7,8,6,10,11,9]
[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] => [12,2,1,3,4,5,7,6,9,10,11,8]
[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] => [12,2,1,3,4,5,6,8,9,10,11,7]
[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] => [12,1,3,4,2,6,5,8,7,10,9,11]
[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] => [12,1,3,4,2,6,5,8,7,9,11,10]
[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] => [12,1,3,4,2,6,5,7,9,10,8,11]
[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] => [12,1,3,4,2,6,5,7,9,8,11,10]
[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] => [12,1,3,4,2,6,5,7,8,10,11,9]
[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] => [12,1,3,4,2,5,7,8,6,10,9,11]
[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] => [12,1,3,4,2,5,7,8,6,9,11,10]
[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] => [12,1,3,4,2,5,7,6,9,10,8,11]
[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] => [12,1,3,4,2,5,7,6,9,8,11,10]
[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] => [12,1,3,4,2,5,7,6,8,10,11,9]
[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] => [12,1,3,4,2,5,6,8,9,10,7,11]
[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] => [12,1,3,4,2,5,6,8,9,7,11,10]
[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] => [12,1,3,4,2,5,6,8,7,10,11,9]
[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] => [12,1,3,4,2,5,6,7,9,10,11,8]
[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] => [12,1,3,2,5,6,4,8,7,10,9,11]
[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] => [12,1,3,2,5,6,4,8,7,9,11,10]
[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] => [12,1,3,2,5,6,4,7,9,10,8,11]
[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] => [12,1,3,2,5,6,4,7,9,8,11,10]
[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] => [12,1,3,2,5,6,4,7,8,10,11,9]
[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] => [12,1,3,2,5,4,7,8,6,10,9,11]
[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] => [12,1,3,2,5,4,7,8,6,9,11,10]
[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] => [12,1,3,2,5,4,7,6,9,10,8,11]
[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] => [12,1,3,2,5,4,7,6,9,8,11,10]
[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] => [12,1,3,2,5,4,7,6,8,10,11,9]
[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] => [12,1,3,2,5,4,6,8,9,10,7,11]
[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] => [12,1,3,2,5,4,6,8,9,7,11,10]
[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] => [12,1,3,2,5,4,6,8,7,10,11,9]
[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] => [12,1,3,2,5,4,6,7,9,10,11,8]
[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] => [12,1,3,2,4,6,7,8,5,10,9,11]
[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] => [12,1,3,2,4,6,7,8,5,9,11,10]
[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] => [12,1,3,2,4,6,7,5,9,10,8,11]
[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] => [12,1,3,2,4,6,7,5,9,8,11,10]
[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] => [12,1,3,2,4,6,7,5,8,10,11,9]
[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] => [12,1,3,2,4,6,5,8,9,10,7,11]
[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] => [12,1,3,2,4,6,5,8,9,7,11,10]
[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] => [12,1,3,2,4,6,5,8,7,10,11,9]
[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] => [12,1,3,2,4,6,5,7,9,10,11,8]
[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] => [12,1,3,2,4,5,7,8,9,10,6,11]
[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] => [12,1,3,2,4,5,7,8,9,6,11,10]
[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] => [12,1,3,2,4,5,7,8,6,10,11,9]
[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] => [12,1,3,2,4,5,7,6,9,10,11,8]
[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] => [12,1,3,2,4,5,6,8,9,10,11,7]
[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] => [12,1,2,4,5,6,3,8,7,10,9,11]
[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] => [12,1,2,4,5,6,3,8,7,9,11,10]
[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] => [12,1,2,4,5,6,3,7,9,10,8,11]
[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] => [12,1,2,4,5,6,3,7,9,8,11,10]
[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] => [12,1,2,4,5,6,3,7,8,10,11,9]
[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] => [12,1,2,4,5,3,7,8,6,10,9,11]
[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] => [12,1,2,4,5,3,7,8,6,9,11,10]
[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] => [12,1,2,4,5,3,7,6,9,10,8,11]
[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] => [12,1,2,4,5,3,7,6,9,8,11,10]
[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] => [12,1,2,4,5,3,7,6,8,10,11,9]
[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] => [12,1,2,4,5,3,6,8,9,10,7,11]
[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] => [12,1,2,4,5,3,6,8,9,7,11,10]
[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] => [12,1,2,4,5,3,6,8,7,10,11,9]
[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] => [12,1,2,4,5,3,6,7,9,10,11,8]
[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] => [12,1,2,4,3,6,7,8,5,10,9,11]
[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] => [12,1,2,4,3,6,7,8,5,9,11,10]
[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] => [12,1,2,4,3,6,7,5,9,10,8,11]
[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] => [12,1,2,4,3,6,7,5,9,8,11,10]
[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] => [12,1,2,4,3,6,7,5,8,10,11,9]
[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] => [12,1,2,4,3,6,5,8,9,10,7,11]
[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] => [12,1,2,4,3,6,5,8,9,7,11,10]
[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] => [12,1,2,4,3,6,5,8,7,10,11,9]
[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] => [12,1,2,4,3,6,5,7,9,10,11,8]
[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] => [12,1,2,4,3,5,7,8,9,10,6,11]
[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] => [12,1,2,4,3,5,7,8,9,6,11,10]
[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] => [12,1,2,4,3,5,7,8,6,10,11,9]
[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] => [12,1,2,4,3,5,7,6,9,10,11,8]
[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] => [12,1,2,4,3,5,6,8,9,10,11,7]
[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] => [12,1,2,3,5,6,7,8,4,10,9,11]
[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] => [12,1,2,3,5,6,7,8,4,9,11,10]
[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] => [12,1,2,3,5,6,7,4,9,10,8,11]
[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] => [12,1,2,3,5,6,7,4,9,8,11,10]
[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] => [12,1,2,3,5,6,7,4,8,10,11,9]
[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] => [12,1,2,3,5,6,4,8,9,10,7,11]
[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] => [12,1,2,3,5,6,4,8,9,7,11,10]
[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] => [12,1,2,3,5,6,4,8,7,10,11,9]
[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] => [12,1,2,3,5,6,4,7,9,10,11,8]
[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] => [12,1,2,3,5,4,7,8,9,10,6,11]
[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] => [12,1,2,3,5,4,7,8,9,6,11,10]
[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] => [12,1,2,3,5,4,7,8,6,10,11,9]
[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] => [12,1,2,3,5,4,7,6,9,10,11,8]
[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] => [12,1,2,3,5,4,6,8,9,10,11,7]
[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] => [12,1,2,3,4,6,7,8,9,10,5,11]
[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] => [12,1,2,3,4,6,7,8,9,5,11,10]
[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] => [12,1,2,3,4,6,7,8,5,10,11,9]
[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] => [12,1,2,3,4,6,7,5,9,10,11,8]
[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] => [12,1,2,3,4,6,5,8,9,10,11,7]
[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] => [12,1,2,3,4,5,7,8,9,10,11,6]
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
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map Φ in [1, sec.3]. In particular, it satisfies
(des,Dbot,Ddif,Res)π=(exc,Ebot,Edif,Ine)Φ(π),
where
  • des is the number of descents, St000021The number of descents of a permutation.,
  • exc is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
  • Dbot is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
  • Ebot is the sum of the excedance bottoms,
  • Ddif is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
  • Edif is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
  • Res is the sum of the (right) embracing numbers,
  • Ine is the sum of the side numbers.