Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Images
[(1,2)] => [2,1] => [1,2] => [[1,2]]
[(1,2),(3,4)] => [2,1,4,3] => [3,4,1,2] => [[1,2],[3,4]]
[(1,3),(2,4)] => [3,4,1,2] => [2,1,4,3] => [[1,3],[2,4]]
[(1,4),(2,3)] => [4,3,2,1] => [1,2,3,4] => [[1,2,3,4]]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,3,6,5,1,2] => [[1,2],[3,5],[4,6]]
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [3,4,5,6,1,2] => [[1,2,5,6],[3,4]]
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [2,4,5,1,6,3] => [[1,3,5,6],[2,4]]
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => [[1,2,3,6],[4,5]]
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]]
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [2,3,1,5,6,4] => [[1,3,4,6],[2,5]]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => [[1,3],[2,5],[4,6]]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [5,6,2,1,4,3] => [[1,3],[2,4],[5,6]]
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [5,6,1,2,3,4] => [[1,2,3,4],[5,6]]
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [4,1,6,2,3,5] => [[1,2,3,5],[4,6]]
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [3,1,2,6,4,5] => [[1,2,4,5],[3,6]]
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]]
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8]]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [6,5,8,7,3,4,1,2] => [[1,2],[3,4],[5,7],[6,8]]
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [5,6,7,8,3,4,1,2] => [[1,2,7,8],[3,4],[5,6]]
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [4,6,7,3,8,5,1,2] => [[1,2,7,8],[3,5],[4,6]]
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [3,6,7,4,5,8,1,2] => [[1,2,5,8],[3,4],[6,7]]
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [2,6,7,4,5,1,8,3] => [[1,3,5,8],[2,4],[6,7]]
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [1,6,7,4,5,2,3,8] => [[1,2,3,8],[4,5],[6,7]]
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [1,5,4,7,6,2,3,8] => [[1,2,3,8],[4,6],[5,7]]
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [2,5,4,7,6,1,8,3] => [[1,3,6,8],[2,4],[5,7]]
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [3,5,4,7,6,8,1,2] => [[1,2,6,8],[3,4],[5,7]]
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [4,5,3,7,8,6,1,2] => [[1,2,6,8],[3,5],[4,7]]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [5,4,3,8,7,6,1,2] => [[1,2],[3,6],[4,7],[5,8]]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [6,4,8,3,7,5,1,2] => [[1,2],[3,5],[4,7],[6,8]]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => [[1,2],[3,5],[4,6],[7,8]]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]]
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [6,3,8,4,5,7,1,2] => [[1,2,5,7],[3,4],[6,8]]
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [5,3,4,8,6,7,1,2] => [[1,2,6,7],[3,4],[5,8]]
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [4,3,5,6,8,7,1,2] => [[1,2,6,7],[3,5],[4,8]]
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [3,4,5,6,7,8,1,2] => [[1,2,5,6,7,8],[3,4]]
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [2,4,5,6,7,1,8,3] => [[1,3,5,6,7,8],[2,4]]
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [1,4,5,6,7,2,3,8] => [[1,2,3,6,7,8],[4,5]]
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [1,3,5,6,2,7,4,8] => [[1,2,4,6,7,8],[3,5]]
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [2,3,5,6,1,7,8,4] => [[1,3,4,6,7,8],[2,5]]
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [3,2,5,6,1,8,7,4] => [[1,4,6,7],[2,5],[3,8]]
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [4,2,5,6,8,1,7,3] => [[1,3,6,7],[2,5],[4,8]]
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [5,2,4,8,6,1,7,3] => [[1,3,6,7],[2,4],[5,8]]
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [6,2,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [7,8,2,4,5,1,6,3] => [[1,3,5,6],[2,4],[7,8]]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [7,8,1,4,5,2,3,6] => [[1,2,3,6],[4,5],[7,8]]
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [6,1,8,4,5,2,3,7] => [[1,2,3,7],[4,5],[6,8]]
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [5,1,4,8,6,2,3,7] => [[1,2,3,7],[4,6],[5,8]]
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [4,1,5,6,8,2,3,7] => [[1,2,3,7],[4,5,6,8]]
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [3,1,5,6,2,8,4,7] => [[1,2,4,7],[3,5,6,8]]
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [2,1,5,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]]
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [1,2,5,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]]
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]]
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]]
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [3,1,4,2,6,8,5,7] => [[1,2,5,7],[3,4,6,8]]
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [4,1,3,2,8,6,5,7] => [[1,2,5,7],[3,6],[4,8]]
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [5,1,3,8,2,6,4,7] => [[1,2,4,7],[3,6],[5,8]]
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [6,1,8,3,2,5,4,7] => [[1,2,4,7],[3,5],[6,8]]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [7,8,1,3,2,5,4,6] => [[1,2,4,6],[3,5],[7,8]]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [7,8,2,3,1,5,6,4] => [[1,3,4,6],[2,5],[7,8]]
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [6,2,8,3,1,5,7,4] => [[1,3,4,7],[2,5],[6,8]]
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]]
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]]
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [3,2,4,1,6,8,7,5] => [[1,4,5,7],[2,6],[3,8]]
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [2,3,4,1,6,7,8,5] => [[1,3,4,5,7,8],[2,6]]
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [1,3,4,2,6,7,5,8] => [[1,2,4,5,7,8],[3,6]]
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]]
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [2,4,3,1,7,6,8,5] => [[1,3,5,8],[2,6],[4,7]]
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [3,4,2,1,7,8,6,5] => [[1,4,5,8],[2,6],[3,7]]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [5,3,2,8,1,7,6,4] => [[1,4],[2,6],[3,7],[5,8]]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [6,3,8,2,1,7,5,4] => [[1,4],[2,5],[3,7],[6,8]]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [7,8,3,2,1,6,5,4] => [[1,4],[2,5],[3,6],[7,8]]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [7,8,4,2,6,1,5,3] => [[1,3],[2,5],[4,6],[7,8]]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [6,4,8,2,7,1,5,3] => [[1,3],[2,5],[4,7],[6,8]]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [5,4,2,8,7,1,6,3] => [[1,3],[2,6],[4,7],[5,8]]
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [4,5,2,7,8,1,6,3] => [[1,3,6,8],[2,5],[4,7]]
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [3,5,2,7,1,8,6,4] => [[1,4,6,8],[2,5],[3,7]]
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [2,5,3,7,1,6,8,4] => [[1,3,4,8],[2,6],[5,7]]
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [1,5,3,7,2,6,4,8] => [[1,2,4,8],[3,6],[5,7]]
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [1,6,7,3,2,5,4,8] => [[1,2,4,8],[3,5],[6,7]]
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [2,6,7,3,1,5,8,4] => [[1,3,4,8],[2,5],[6,7]]
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [3,6,7,2,1,8,5,4] => [[1,4,7,8],[2,5],[3,6]]
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [4,6,7,2,8,1,5,3] => [[1,3,7,8],[2,5],[4,6]]
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [5,6,7,8,2,1,4,3] => [[1,3,7,8],[2,4],[5,6]]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => [[1,3],[2,4],[5,7],[6,8]]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [7,8,5,6,2,1,4,3] => [[1,3],[2,4],[5,6],[7,8]]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [7,8,5,6,1,2,3,4] => [[1,2,3,4],[5,6],[7,8]]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [6,5,8,7,1,2,3,4] => [[1,2,3,4],[5,7],[6,8]]
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]]
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [4,6,7,1,8,2,3,5] => [[1,2,3,5],[4,6,7,8]]
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [3,6,7,1,2,8,4,5] => [[1,2,4,5],[3,6,7,8]]
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [2,6,7,1,3,4,8,5] => [[1,3,4,5],[2,6,7,8]]
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [1,6,7,2,3,4,5,8] => [[1,2,3,4,5,8],[6,7]]
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [1,5,2,7,3,4,6,8] => [[1,2,3,4,6,8],[5,7]]
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [2,5,1,7,3,4,8,6] => [[1,3,4,6],[2,5,7,8]]
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [3,5,1,7,2,8,4,6] => [[1,2,4,6],[3,5,7,8]]
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [4,5,1,7,8,2,3,6] => [[1,2,3,6],[4,5,7,8]]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [5,4,1,8,7,2,3,6] => [[1,2,3,6],[4,7],[5,8]]
>>> Load all 141 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [6,4,8,1,7,2,3,5] => [[1,2,3,5],[4,7],[6,8]]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [7,8,4,1,6,2,3,5] => [[1,2,3,5],[4,6],[7,8]]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [7,8,3,1,2,6,4,5] => [[1,2,4,5],[3,6],[7,8]]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [6,3,8,1,2,7,4,5] => [[1,2,4,5],[3,7],[6,8]]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [5,3,1,8,2,7,4,6] => [[1,2,4,6],[3,7],[5,8]]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [4,3,1,2,8,7,5,6] => [[1,2,5,6],[3,7],[4,8]]
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [3,4,1,2,7,8,5,6] => [[1,2,5,6],[3,4,7,8]]
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [2,4,1,3,7,5,8,6] => [[1,3,5,6],[2,4,7,8]]
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [1,4,2,3,7,5,6,8] => [[1,2,3,5,6,8],[4,7]]
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]]
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [2,3,1,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]]
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]]
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [4,2,1,3,8,5,7,6] => [[1,3,5,6],[2,7],[4,8]]
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [5,2,1,8,3,4,7,6] => [[1,3,4,6],[2,7],[5,8]]
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [6,2,8,1,3,4,7,5] => [[1,3,4,5],[2,7],[6,8]]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [7,8,2,1,3,4,6,5] => [[1,3,4,5],[2,6],[7,8]]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [7,8,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8]]
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [6,1,8,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8]]
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [5,1,2,8,3,4,6,7] => [[1,2,3,4,6,7],[5,8]]
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [4,1,2,3,8,5,6,7] => [[1,2,3,5,6,7],[4,8]]
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [3,1,2,4,5,8,6,7] => [[1,2,4,5,6,7],[3,8]]
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]]
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]]
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]]
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [9,10,3,4,5,6,7,8,1,2] => [[1,2,5,6,7,8],[3,4],[9,10]]
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [3,4,5,6,7,8,9,10,1,2] => [[1,2,5,6,7,8,9,10],[3,4]]
[(1,3),(2,9),(4,7),(5,6),(8,10)] => [3,9,1,7,6,5,4,10,2,8] => [8,2,10,4,5,6,7,1,9,3] => [[1,3,5,6,7,9],[2,4],[8,10]]
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]]
[(1,9),(2,8),(3,7),(4,6),(5,10)] => [9,8,7,6,10,4,3,2,1,5] => [2,3,4,5,1,7,8,9,10,6] => [[1,3,4,5,6,8,9,10],[2,7]]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]]
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [5,6,7,8,9,10,1,2,3,4] => [[1,2,3,4,9,10],[5,6,7,8]]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [7,8,9,10,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]]
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [9,10,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]]
[(1,6),(2,10),(3,9),(4,8),(5,7)] => [6,10,9,8,7,1,5,4,3,2] => [5,1,2,3,4,10,6,7,8,9] => [[1,2,3,4,6,7,8,9],[5,10]]
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [9,10,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,10,9] => [[1,3,4,5,6,7,8,9],[2,10]]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [11,12,1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10],[11,12]]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [7,8,9,10,11,12,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [6,5,4,3,2,1,12,11,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion 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 insertion tableau.