Processing math: 100%

Identifier
Mp00283: Perfect matchings non-nesting-exceedence permutationPermutations
Mp00070: Permutations Robinson-Schensted recording tableauStandard tableaux
Mp00085: Standard tableaux Schützenberger involution Standard tableaux
Images
[(1,2)] => [2,1] => [[1],[2]] => [[1],[2]]
[(1,2),(3,4)] => [2,1,4,3] => [[1,3],[2,4]] => [[1,3],[2,4]]
[(1,3),(2,4)] => [3,4,1,2] => [[1,2],[3,4]] => [[1,2],[3,4]]
[(1,4),(2,3)] => [3,4,2,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => [[1,3,5],[2,4,6]]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => [[1,3,4],[2,5,6]]
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [[1,2,5],[3,6],[4]] => [[1,3,6],[2,4],[5]]
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [[1,2,4],[3,6],[5]] => [[1,2,6],[3,4],[5]]
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [[1,2,4],[3,5],[6]] => [[1,4,6],[2,5],[3]]
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [[1,2,3],[4,5],[6]] => [[1,3,6],[2,5],[4]]
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [[1,2,3],[4,6],[5]] => [[1,2,6],[3,5],[4]]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => [[1,2,3],[4,5,6]]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => [[1,2,4],[3,5,6]]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => [[1,2,5],[3,4,6]]
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [[1,3,4],[2,5],[6]] => [[1,4,5],[2,6],[3]]
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [[1,2,4],[3,5],[6]] => [[1,4,6],[2,5],[3]]
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [[1,2,3],[4,5],[6]] => [[1,3,6],[2,5],[4]]
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [[1,2,3],[4,6],[5]] => [[1,2,6],[3,5],[4]]
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => [[1,5,6],[2],[3],[4]]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [[1,3,5,7],[2,4,6,8]]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => [[1,3,5,6],[2,4,7,8]]
[(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]] => [[1,3,5,8],[2,4,6],[7]]
[(1,5),(2,3),(4,6),(7,8)] => [3,5,2,6,1,4,8,7] => [[1,2,4,7],[3,6,8],[5]] => [[1,3,4,8],[2,5,6],[7]]
[(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]]
[(1,7),(2,3),(4,5),(6,8)] => [3,5,2,7,4,8,1,6] => [[1,2,4,6],[3,5,8],[7]] => [[1,2,6,8],[3,4,7],[5]]
[(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]
[(1,8),(2,4),(3,5),(6,7)] => [4,5,7,2,3,8,6,1] => [[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]]
[(1,7),(2,4),(3,5),(6,8)] => [4,5,7,2,3,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => [[1,2,5,8],[3,4,7],[6]]
[(1,6),(2,4),(3,5),(7,8)] => [4,5,6,2,3,1,8,7] => [[1,2,3,7],[4,5,8],[6]] => [[1,3,5,8],[2,4,7],[6]]
[(1,5),(2,4),(3,6),(7,8)] => [4,5,6,2,1,3,8,7] => [[1,2,3,7],[4,6,8],[5]] => [[1,3,4,8],[2,5,7],[6]]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [[1,2,3,7],[4,5,6,8]] => [[1,3,4,5],[2,6,7,8]]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]] => [[1,3,4,6],[2,5,7,8]]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]] => [[1,3,4,7],[2,5,6,8]]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => [[1,3,6,7],[2,4,8],[5]]
[(1,3),(2,6),(4,5),(7,8)] => [3,5,1,6,4,2,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]]
[(1,4),(2,6),(3,5),(7,8)] => [4,5,6,1,3,2,8,7] => [[1,2,3,7],[4,5,8],[6]] => [[1,3,5,8],[2,4,7],[6]]
[(1,5),(2,6),(3,4),(7,8)] => [4,5,6,3,1,2,8,7] => [[1,2,3,7],[4,6,8],[5]] => [[1,3,4,8],[2,5,7],[6]]
[(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,3,7,8],[2,4],[5],[6]]
[(1,7),(2,5),(3,4),(6,8)] => [4,5,7,3,2,8,1,6] => [[1,2,3,6],[4,8],[5],[7]] => [[1,2,7,8],[3,4],[5],[6]]
[(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [[1,2,3,6],[4,7],[5],[8]] => [[1,4,7,8],[2,5],[3],[6]]
[(1,8),(2,6),(3,4),(5,7)] => [4,6,7,3,8,2,5,1] => [[1,2,3,5],[4,7],[6],[8]] => [[1,3,7,8],[2,5],[4],[6]]
[(1,7),(2,6),(3,4),(5,8)] => [4,6,7,3,8,2,1,5] => [[1,2,3,5],[4,8],[6],[7]] => [[1,2,7,8],[3,5],[4],[6]]
[(1,6),(2,7),(3,4),(5,8)] => [4,6,7,3,8,1,2,5] => [[1,2,3,5],[4,7,8],[6]] => [[1,2,3,8],[4,5,7],[6]]
[(1,5),(2,7),(3,4),(6,8)] => [4,5,7,3,1,8,2,6] => [[1,2,3,6],[4,7,8],[5]] => [[1,2,4,8],[3,5,7],[6]]
[(1,4),(2,7),(3,5),(6,8)] => [4,5,7,1,3,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => [[1,2,5,8],[3,4,7],[6]]
[(1,3),(2,7),(4,5),(6,8)] => [3,5,1,7,4,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => [[1,2,6,8],[3,4,7],[5]]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,5,7,4,8,3,6] => [[1,3,4,6],[2,5,8],[7]] => [[1,2,6,7],[3,4,8],[5]]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]
[(1,3),(2,8),(4,5),(6,7)] => [3,5,1,7,4,8,6,2] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]
[(1,4),(2,8),(3,5),(6,7)] => [4,5,7,1,3,8,6,2] => [[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]]
[(1,5),(2,8),(3,4),(6,7)] => [4,5,7,3,1,8,6,2] => [[1,2,3,6],[4,7],[5,8]] => [[1,4,7,8],[2,5],[3,6]]
[(1,6),(2,8),(3,4),(5,7)] => [4,6,7,3,8,1,5,2] => [[1,2,3,5],[4,7],[6,8]] => [[1,3,7,8],[2,5],[4,6]]
[(1,7),(2,8),(3,4),(5,6)] => [4,6,7,3,8,5,1,2] => [[1,2,3,5],[4,6],[7,8]] => [[1,2,7,8],[3,5],[4,6]]
[(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [[1,2,3,5],[4,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]]
[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,4,7,8],[2,6],[3],[5]]
[(1,7),(2,8),(3,5),(4,6)] => [5,6,7,8,3,4,1,2] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,7,8],[3,4],[5,6]]
[(1,6),(2,8),(3,5),(4,7)] => [5,6,7,8,3,1,4,2] => [[1,2,3,4],[5,7],[6,8]] => [[1,3,7,8],[2,4],[5,6]]
[(1,5),(2,8),(3,6),(4,7)] => [5,6,7,8,1,3,4,2] => [[1,2,3,4],[5,6,7],[8]] => [[1,3,4,8],[2,6,7],[5]]
[(1,4),(2,8),(3,6),(5,7)] => [4,6,7,1,8,3,5,2] => [[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]]
[(1,3),(2,8),(4,6),(5,7)] => [3,6,1,7,8,4,5,2] => [[1,2,4,5],[3,6,7],[8]] => [[1,3,6,8],[2,5,7],[4]]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,6,7,8,4,5,3] => [[1,3,4,5],[2,6,7],[8]] => [[1,3,6,7],[2,5,8],[4]]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,6,7,8,4,3,5] => [[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]]
[(1,3),(2,7),(4,6),(5,8)] => [3,6,1,7,8,4,2,5] => [[1,2,4,5],[3,6,8],[7]] => [[1,2,6,8],[3,5,7],[4]]
[(1,4),(2,7),(3,6),(5,8)] => [4,6,7,1,8,3,2,5] => [[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]]
[(1,5),(2,7),(3,6),(4,8)] => [5,6,7,8,1,3,2,4] => [[1,2,3,4],[5,6,8],[7]] => [[1,2,4,8],[3,6,7],[5]]
[(1,6),(2,7),(3,5),(4,8)] => [5,6,7,8,3,1,2,4] => [[1,2,3,4],[5,7,8],[6]] => [[1,2,3,8],[4,6,7],[5]]
[(1,7),(2,6),(3,5),(4,8)] => [5,6,7,8,3,2,1,4] => [[1,2,3,4],[5,8],[6],[7]] => [[1,2,7,8],[3,6],[4],[5]]
[(1,8),(2,6),(3,5),(4,7)] => [5,6,7,8,3,2,4,1] => [[1,2,3,4],[5,7],[6],[8]] => [[1,3,7,8],[2,6],[4],[5]]
[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => [[1,2,3,4],[5,6,7],[8]] => [[1,3,4,8],[2,6,7],[5]]
[(1,7),(2,5),(3,6),(4,8)] => [5,6,7,8,2,3,1,4] => [[1,2,3,4],[5,6,8],[7]] => [[1,2,4,8],[3,6,7],[5]]
[(1,6),(2,5),(3,7),(4,8)] => [5,6,7,8,2,1,3,4] => [[1,2,3,4],[5,7,8],[6]] => [[1,2,3,8],[4,6,7],[5]]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]] => [[1,2,3,4],[5,6,7,8]]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [[1,2,3,5],[4,6,7,8]] => [[1,2,3,5],[4,6,7,8]]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [[1,2,4,5],[3,6,7,8]] => [[1,2,3,6],[4,5,7,8]]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [[1,3,4,5],[2,6,7,8]] => [[1,2,3,7],[4,5,6,8]]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [[1,3,4,6],[2,5,7,8]] => [[1,2,4,7],[3,5,6,8]]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [[1,2,4,6],[3,5,7,8]] => [[1,2,4,6],[3,5,7,8]]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [[1,2,3,6],[4,5,7,8]] => [[1,2,4,5],[3,6,7,8]]
[(1,5),(2,4),(3,7),(6,8)] => [4,5,7,2,1,8,3,6] => [[1,2,3,6],[4,7,8],[5]] => [[1,2,4,8],[3,5,7],[6]]
[(1,6),(2,4),(3,7),(5,8)] => [4,6,7,2,8,1,3,5] => [[1,2,3,5],[4,7,8],[6]] => [[1,2,3,8],[4,5,7],[6]]
[(1,7),(2,4),(3,6),(5,8)] => [4,6,7,2,8,3,1,5] => [[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]]
[(1,8),(2,4),(3,6),(5,7)] => [4,6,7,2,8,3,5,1] => [[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]]
[(1,8),(2,3),(4,6),(5,7)] => [3,6,2,7,8,4,5,1] => [[1,2,4,5],[3,6,7],[8]] => [[1,3,6,8],[2,5,7],[4]]
[(1,7),(2,3),(4,6),(5,8)] => [3,6,2,7,8,4,1,5] => [[1,2,4,5],[3,6,8],[7]] => [[1,2,6,8],[3,5,7],[4]]
[(1,6),(2,3),(4,7),(5,8)] => [3,6,2,7,8,1,4,5] => [[1,2,4,5],[3,7,8],[6]] => [[1,2,3,8],[4,5,6],[7]]
[(1,5),(2,3),(4,7),(6,8)] => [3,5,2,7,1,8,4,6] => [[1,2,4,6],[3,7,8],[5]] => [[1,2,4,8],[3,5,6],[7]]
[(1,4),(2,3),(5,7),(6,8)] => [3,4,2,1,7,8,5,6] => [[1,2,5,6],[3,7,8],[4]] => [[1,2,5,8],[3,4,6],[7]]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [[1,2,5,6],[3,4,7,8]] => [[1,2,5,6],[3,4,7,8]]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [[1,3,5,6],[2,4,7,8]] => [[1,2,5,7],[3,4,6,8]]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,7,8,6,5] => [[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]]
[(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]]
[(1,5),(2,3),(4,8),(6,7)] => [3,5,2,7,1,8,6,4] => [[1,2,4,6],[3,7],[5,8]] => [[1,4,6,8],[2,5],[3,7]]
[(1,6),(2,3),(4,8),(5,7)] => [3,6,2,7,8,1,5,4] => [[1,2,4,5],[3,7],[6,8]] => [[1,3,6,8],[2,5],[4,7]]
[(1,7),(2,3),(4,8),(5,6)] => [3,6,2,7,8,5,1,4] => [[1,2,4,5],[3,6],[7,8]] => [[1,2,6,8],[3,5],[4,7]]
[(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [[1,2,4,5],[3,6],[7],[8]] => [[1,5,6,8],[2,7],[3],[4]]
[(1,8),(2,4),(3,7),(5,6)] => [4,6,7,2,8,5,3,1] => [[1,2,3,5],[4,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]]
[(1,7),(2,4),(3,8),(5,6)] => [4,6,7,2,8,5,1,3] => [[1,2,3,5],[4,6],[7,8]] => [[1,2,7,8],[3,5],[4,6]]
[(1,6),(2,4),(3,8),(5,7)] => [4,6,7,2,8,1,5,3] => [[1,2,3,5],[4,7],[6,8]] => [[1,3,7,8],[2,5],[4,6]]
[(1,5),(2,4),(3,8),(6,7)] => [4,5,7,2,1,8,6,3] => [[1,2,3,6],[4,7],[5,8]] => [[1,4,7,8],[2,5],[3,6]]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,7,1,2,8,6,3] => [[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]]
>>> Load all 141 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,7,2,8,6,4] => [[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,7,3,8,6,4] => [[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,7,8,3,5,4] => [[1,3,4,5],[2,6,7],[8]] => [[1,3,6,7],[2,5,8],[4]]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,7,8,2,5,4] => [[1,2,4,5],[3,6,7],[8]] => [[1,3,6,8],[2,5,7],[4]]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,7,1,8,2,5,3] => [[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,7,8,1,2,4,3] => [[1,2,3,4],[5,6,7],[8]] => [[1,3,4,8],[2,6,7],[5]]
[(1,6),(2,5),(3,8),(4,7)] => [5,6,7,8,2,1,4,3] => [[1,2,3,4],[5,7],[6,8]] => [[1,3,7,8],[2,4],[5,6]]
[(1,7),(2,5),(3,8),(4,6)] => [5,6,7,8,2,4,1,3] => [[1,2,3,4],[5,6],[7,8]] => [[1,2,7,8],[3,4],[5,6]]
[(1,8),(2,5),(3,7),(4,6)] => [5,6,7,8,2,4,3,1] => [[1,2,3,4],[5,6],[7],[8]] => [[1,4,7,8],[2,6],[3],[5]]
[(1,8),(2,6),(3,7),(4,5)] => [5,6,7,8,4,2,3,1] => [[1,2,3,4],[5,7],[6],[8]] => [[1,3,7,8],[2,6],[4],[5]]
[(1,7),(2,6),(3,8),(4,5)] => [5,6,7,8,4,2,1,3] => [[1,2,3,4],[5,8],[6],[7]] => [[1,2,7,8],[3,6],[4],[5]]
[(1,6),(2,7),(3,8),(4,5)] => [5,6,7,8,4,1,2,3] => [[1,2,3,4],[5,7,8],[6]] => [[1,2,3,8],[4,6,7],[5]]
[(1,5),(2,7),(3,8),(4,6)] => [5,6,7,8,1,4,2,3] => [[1,2,3,4],[5,6,8],[7]] => [[1,2,4,8],[3,6,7],[5]]
[(1,4),(2,7),(3,8),(5,6)] => [4,6,7,1,8,5,2,3] => [[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]]
[(1,3),(2,7),(4,8),(5,6)] => [3,6,1,7,8,5,2,4] => [[1,2,4,5],[3,6,8],[7]] => [[1,2,6,8],[3,5,7],[4]]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,6,7,8,5,3,4] => [[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [[1,3,4,5],[2,6],[7],[8]] => [[1,5,6,7],[2,8],[3],[4]]
[(1,3),(2,8),(4,7),(5,6)] => [3,6,1,7,8,5,4,2] => [[1,2,4,5],[3,6],[7],[8]] => [[1,5,6,8],[2,7],[3],[4]]
[(1,4),(2,8),(3,7),(5,6)] => [4,6,7,1,8,5,3,2] => [[1,2,3,5],[4,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]]
[(1,5),(2,8),(3,7),(4,6)] => [5,6,7,8,1,4,3,2] => [[1,2,3,4],[5,6],[7],[8]] => [[1,4,7,8],[2,6],[3],[5]]
[(1,6),(2,8),(3,7),(4,5)] => [5,6,7,8,4,1,3,2] => [[1,2,3,4],[5,7],[6],[8]] => [[1,3,7,8],[2,6],[4],[5]]
[(1,7),(2,8),(3,6),(4,5)] => [5,6,7,8,4,3,1,2] => [[1,2,3,4],[5,8],[6],[7]] => [[1,2,7,8],[3,6],[4],[5]]
[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5]]
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => [[1,3,5,7,9],[2,4,6,8,10]]
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [[1,2,5,7,9],[3,4,6,8,10]] => [[1,3,5,7,8],[2,4,6,9,10]]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [3,4,2,1,6,5,8,7,10,9] => [[1,2,5,7,9],[3,6,8,10],[4]] => [[1,3,5,7,10],[2,4,6,8],[9]]
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [3,5,2,7,4,8,6,1,10,9] => [[1,2,4,6,9],[3,5,7,10],[8]] => [[1,3,6,8,10],[2,4,7,9],[5]]
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [3,5,2,7,4,9,6,10,8,1] => [[1,2,4,6,8],[3,5,7,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]]
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [4,6,8,3,9,5,10,7,2,1] => [[1,2,3,5,7],[4,6,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]]
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [5,7,8,9,4,10,6,3,2,1] => [[1,2,3,4,6],[5,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]]
[(1,6),(2,10),(3,9),(4,7),(5,8)] => [6,7,8,9,10,1,4,5,3,2] => [[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,4,5,9,10],[2,7,8],[3],[6]]
[(1,6),(2,9),(3,10),(4,7),(5,8)] => [6,7,8,9,10,1,4,5,2,3] => [[1,2,3,4,5],[6,7,8],[9,10]] => [[1,2,5,9,10],[3,4,8],[6,7]]
[(1,9),(2,8),(3,7),(4,6),(5,10)] => [6,7,8,9,10,4,3,2,1,5] => [[1,2,3,4,5],[6,10],[7],[8],[9]] => [[1,2,8,9,10],[3,7],[4],[5],[6]]
[(1,6),(2,10),(3,7),(4,8),(5,9)] => [6,7,8,9,10,1,3,4,5,2] => [[1,2,3,4,5],[6,7,8,9],[10]] => [[1,3,4,5,10],[2,7,8,9],[6]]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9,10]] => [[1,2,3,4,5],[6,7,8,9,10]]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [3,4,2,1,8,9,10,7,6,5] => [[1,2,5,6,7],[3,8],[4,9],[10]] => [[1,5,6,7,10],[2,8],[3,9],[4]]
[(1,6),(2,10),(3,9),(4,8),(5,7)] => [6,7,8,9,10,1,5,4,3,2] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,7],[3],[4],[6]]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [6,7,8,9,10,5,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,7,8,9,10],[2],[3],[4],[5],[6]]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,3,5,7,9,11],[2,4,6,8,10,12]]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.