Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00237: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Images
[(1,2)] => [2,1] => [2,1] => [[1],[2]]
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [[1,3],[2,4]]
[(1,3),(2,4)] => [3,4,1,2] => [4,1,3,2] => [[1,2],[3],[4]]
[(1,4),(2,3)] => [4,3,2,1] => [2,3,4,1] => [[1,3,4],[2]]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => [[1,2,5],[3,6],[4]]
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => [[1,3,4,5],[2,6]]
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => [[1,2,4],[3,5],[6]]
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [4,3,5,6,1,2] => [[1,2,6],[3,5],[4]]
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [3,5,2,6,4,1] => [[1,4,6],[2,5],[3]]
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [2,6,1,5,4,3] => [[1,3],[2,4],[5],[6]]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [[1,2,3,5],[4],[6]]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [5,6,3,2,1,4] => [[1,4],[2,6],[3],[5]]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => [[1,3,4],[2,5],[6]]
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => [[1,3,5,6],[2,4]]
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [6,4,3,5,1,2] => [[1,2],[3,5],[4],[6]]
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [5,3,1,4,6,2] => [[1,2,6],[3,4],[5]]
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [3,1,4,6,5,2] => [[1,2,5],[3,4],[6]]
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [[1,3,4,5,6],[2]]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]]
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [[1,3,4,5,7],[2,6,8]]
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [6,3,5,1,2,4,8,7] => [[1,2,4,7],[3,5,8],[6]]
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [4,3,5,6,1,2,8,7] => [[1,2,6,7],[3,5,8],[4]]
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [8,3,7,5,2,1,4,6] => [[1,4,6],[2,5],[3],[7],[8]]
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [6,3,7,5,2,8,1,4] => [[1,4,8],[2,5],[3,7],[6]]
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [6,5,2,7,4,8,1,3] => [[1,3,8],[2,4],[5,7],[6]]
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [8,5,2,7,4,1,3,6] => [[1,3,6],[2,4],[5,7],[8]]
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [3,5,2,6,4,1,8,7] => [[1,4,6,7],[2,5,8],[3]]
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [2,6,1,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [6,1,2,4,5,3,8,7] => [[1,2,3,5,7],[4,8],[6]]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [5,6,3,2,1,4,8,7] => [[1,4,7],[2,6,8],[3],[5]]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => [[1,3,4,7],[2,5,8],[6]]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => [[1,3,5,6,7],[2,4,8]]
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [6,4,3,5,1,2,8,7] => [[1,2,7],[3,5,8],[4],[6]]
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [5,3,1,4,6,2,8,7] => [[1,2,6,7],[3,4,8],[5]]
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [3,1,4,6,5,2,8,7] => [[1,2,5,7],[3,4,8],[6]]
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => [[1,3,4,5,6,7],[2,8]]
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [8,3,4,5,7,1,2,6] => [[1,2,5,6],[3,4,7],[8]]
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [6,3,4,5,7,8,1,2] => [[1,2,5,7,8],[3,4],[6]]
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [5,7,4,6,2,8,3,1] => [[1,3,8],[2,6],[4,7],[5]]
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [2,8,4,6,1,7,3,5] => [[1,3,5,7],[2,4,6],[8]]
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [8,1,4,7,2,6,3,5] => [[1,2,3,5],[4,6],[7],[8]]
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [3,4,7,8,5,2,1,6] => [[1,4,5,6],[2,8],[3],[7]]
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [5,7,1,4,8,3,2,6] => [[1,2,6],[3,7,8],[4],[5]]
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [7,8,3,5,1,4,6,2] => [[1,2,6],[3,4],[5,8],[7]]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,8,5,7,3,4,6] => [[1,3,4,6],[2,5,7],[8]]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,6,5,7,8,3,4] => [[1,3,4,8],[2,5,7],[6]]
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [8,6,3,5,1,7,4,2] => [[1,2,7],[3,4],[5],[6],[8]]
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [5,8,1,4,6,7,2,3] => [[1,2,3,7],[4,6],[5,8]]
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [3,4,8,6,5,7,1,2] => [[1,2,5,7],[3,4],[6],[8]]
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [7,5,4,8,1,6,3,2] => [[1,2],[3,6],[4,8],[5],[7]]
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [5,1,4,6,8,2,7,3] => [[1,2,3,7],[4,6],[5,8]]
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [2,5,4,6,7,1,8,3] => [[1,3,6,7,8],[2,4],[5]]
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [2,4,6,3,7,5,8,1] => [[1,3,5,7,8],[2,6],[4]]
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [4,1,6,3,8,5,7,2] => [[1,2,5,7],[3,6,8],[4]]
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [3,7,4,2,8,6,5,1] => [[1,4,5],[2,6],[3,8],[7]]
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [7,4,1,3,5,8,6,2] => [[1,2,5,6],[3,8],[4],[7]]
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [6,5,8,4,3,7,2,1] => [[1,7],[2,8],[3],[4],[5],[6]]
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [8,5,3,7,4,1,6,2] => [[1,2,6],[3,4],[5,7],[8]]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,5,7,4,8,6,3] => [[1,3,6,8],[2,4,7],[5]]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,4,8,3,7,6,5] => [[1,3,5],[2,4,6],[7],[8]]
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [7,4,3,8,2,1,6,5] => [[1,5],[2,6],[3,8],[4],[7]]
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [6,3,7,4,2,8,5,1] => [[1,4,5],[2,7,8],[3],[6]]
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [8,3,1,2,5,7,6,4] => [[1,2,4,6],[3,5],[7],[8]]
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [3,1,8,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]]
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [2,3,8,1,6,7,5,4] => [[1,3,4,7],[2,5],[6],[8]]
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [4,3,7,2,6,8,5,1] => [[1,5,8],[2,6],[3,7],[4]]
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [4,7,2,3,8,5,6,1] => [[1,3,5,6],[2,7,8],[4]]
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [3,8,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7],[8]]
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [2,8,1,3,6,5,7,4] => [[1,3,4,7],[2,5],[6],[8]]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [7,8,2,4,3,6,1,5] => [[1,3,5],[2,6],[4,8],[7]]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [6,8,3,2,4,1,7,5] => [[1,4,5],[2,7],[3,8],[6]]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,8,3,4,6,7,5] => [[1,3,4,5,7],[2,6],[8]]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,4,3,6] => [[1,3,6],[2,4,8],[5],[7]]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,4,2,6] => [[1,2,6],[3,4,8],[5,7]]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [7,1,8,4,5,3,2,6] => [[1,2,5,6],[3,8],[4],[7]]
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [2,7,8,5,4,3,1,6] => [[1,3,6],[2,8],[4],[5],[7]]
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [8,7,1,6,2,4,5,3] => [[1,2,3,5],[4],[6],[7],[8]]
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [3,8,6,7,1,4,5,2] => [[1,2,5],[3,4,7],[6],[8]]
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [5,6,7,8,3,4,2,1] => [[1,4,7,8],[2,6],[3],[5]]
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [5,3,8,7,4,1,2,6] => [[1,2,6],[3,4],[5,7],[8]]
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [4,3,8,7,1,5,6,2] => [[1,2,6],[3,5],[4,7],[8]]
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [8,3,6,1,2,5,7,4] => [[1,2,4,7],[3,5],[6],[8]]
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [7,3,5,8,2,4,1,6] => [[1,4,6],[2,5,8],[3],[7]]
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [2,3,4,1,8,5,7,6] => [[1,3,4,5,6],[2,7],[8]]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => [[1,2,5,6],[3,7],[4,8]]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,5,7,6] => [[1,3,5,6],[2,4,7],[8]]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => [[1,3,5,7,8],[2,4,6]]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [4,1,3,2,6,7,8,5] => [[1,2,5,7,8],[3,6],[4]]
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => [[1,3,4,5,7,8],[2,6]]
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [8,3,5,6,2,7,1,4] => [[1,4,6,7],[2,5],[3],[8]]
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [7,3,6,5,1,2,8,4] => [[1,2,4],[3,5,8],[6],[7]]
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [5,3,6,1,8,7,2,4] => [[1,2,4],[3,6,7],[5,8]]
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [4,3,5,6,7,8,1,2] => [[1,2,6,7,8],[3,5],[4]]
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [3,5,6,7,8,2,1,4] => [[1,4,6,7,8],[2,5],[3]]
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [5,6,1,8,7,3,2,4] => [[1,2,4],[3,6,7],[5],[8]]
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [7,8,5,6,1,4,2,3] => [[1,2,3],[4,6],[5,8],[7]]
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [2,8,6,5,4,7,1,3] => [[1,3,7],[2,4],[5],[6],[8]]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [8,1,6,4,5,7,2,3] => [[1,2,3,7],[4,5],[6],[8]]
>>> Load all 288 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [5,8,3,6,1,7,2,4] => [[1,2,4],[3,6,7],[5,8]]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,8,6,5,7,3,4] => [[1,3,4],[2,5,7],[6],[8]]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,7,5,3,6,8,4] => [[1,3,4,8],[2,5,6],[7]]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [6,7,3,5,2,1,8,4] => [[1,4,8],[2,5],[3,7],[6]]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [8,7,5,4,2,6,1,3] => [[1,3],[2,6],[4],[5],[7],[8]]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [7,1,4,2,5,6,8,3] => [[1,2,3,6,8],[4,5],[7]]
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [2,7,4,1,6,5,8,3] => [[1,3,5,8],[2,4],[6],[7]]
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [4,6,1,2,8,7,3,5] => [[1,2,3,5],[4,6,7],[8]]
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [3,4,6,1,7,8,2,5] => [[1,2,5,7,8],[3,4,6]]
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [3,4,2,5,7,8,6,1] => [[1,4,5,6,8],[2,7],[3]]
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [2,4,1,5,8,7,6,3] => [[1,3,5,6],[2,4],[7],[8]]
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [4,1,2,5,8,6,7,3] => [[1,2,3,6,7],[4,5],[8]]
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [6,4,2,1,5,8,7,3] => [[1,3,7],[2,5],[4,8],[6]]
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [8,5,2,4,6,1,7,3] => [[1,3,6,7],[2,4],[5],[8]]
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [7,5,3,2,6,8,1,4] => [[1,4,8],[2,6],[3],[5],[7]]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,5,3,6,8,7,4] => [[1,3,4,7],[2,5,6],[8]]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]]
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [8,4,3,5,6,7,1,2] => [[1,2,6,7],[3,5],[4],[8]]
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [7,3,5,4,6,1,8,2] => [[1,2,6,8],[3,4],[5],[7]]
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [6,3,4,1,5,7,8,2] => [[1,2,5,7,8],[3,4],[6]]
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [4,3,1,5,7,6,8,2] => [[1,2,6,8],[3,5],[4,7]]
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [3,1,4,5,6,8,7,2] => [[1,2,5,6,7],[3,4],[8]]
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2]]
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[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] => [4,1,3,2,6,5,8,7,10,9] => [[1,2,5,7,9],[3,6,8,10],[4]]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => [[1,3,4,5,7,9],[2,6,8,10]]
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [4,3,5,6,1,2,8,7,10,9] => [[1,2,6,7,9],[3,5,8,10],[4]]
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [6,1,2,4,5,3,8,7,10,9] => [[1,2,3,5,7,9],[4,8,10],[6]]
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,6,3,5,4,8,7,10,9] => [[1,3,4,7,9],[2,5,8,10],[6]]
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,4,5,6,3,8,7,10,9] => [[1,3,5,6,7,9],[2,4,8,10]]
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [2,3,4,5,6,1,8,7,10,9] => [[1,3,4,5,6,7,9],[2,8,10]]
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [6,3,4,5,7,8,1,2,10,9] => [[1,2,5,7,8,9],[3,4,10],[6]]
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [2,1,6,5,7,8,3,4,10,9] => [[1,3,4,8,9],[2,5,7,10],[6]]
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [2,5,4,6,7,1,8,3,10,9] => [[1,3,6,7,8,9],[2,4,10],[5]]
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [8,1,2,3,5,6,7,4,10,9] => [[1,2,3,4,6,7,9],[5,10],[8]]
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,8,3,4,6,7,5,10,9] => [[1,3,4,5,7,9],[2,6,10],[8]]
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [4,1,3,2,8,5,7,6,10,9] => [[1,2,5,6,9],[3,7,10],[4,8]]
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,8,5,7,6,10,9] => [[1,3,5,6,9],[2,4,7,10],[8]]
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,6,7,8,5,10,9] => [[1,3,5,7,8,9],[2,4,6,10]]
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9] => [[1,3,4,5,7,8,9],[2,6,10]]
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [4,3,5,6,7,8,1,2,10,9] => [[1,2,6,7,8,9],[3,5,10],[4]]
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9] => [[1,3,5,6,7,8,9],[2,4,10]]
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9] => [[1,3,4,5,6,7,8,9],[2,10]]
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [10,3,4,5,6,7,9,1,2,8] => [[1,2,5,6,7,8],[3,4,9],[10]]
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [8,3,4,5,6,7,9,10,1,2] => [[1,2,5,6,7,9,10],[3,4],[8]]
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [2,1,8,5,6,7,9,10,3,4] => [[1,3,4,7,9,10],[2,5,6],[8]]
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [2,7,4,5,6,8,9,1,10,3] => [[1,3,5,6,8,9,10],[2,4],[7]]
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [2,1,4,3,8,7,9,10,5,6] => [[1,3,5,6,10],[2,4,7,9],[8]]
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [2,3,4,1,8,7,9,10,5,6] => [[1,3,4,5,6,10],[2,7,9],[8]]
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,4,7,6,8,9,3,10,5] => [[1,3,5,8,9,10],[2,4,6],[7]]
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [2,3,6,5,7,8,1,9,10,4] => [[1,3,4,7,8,9,10],[2,5],[6]]
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [3,5,2,7,4,9,6,10,8,1] => [[1,4,6,8,10],[2,5,7,9],[3]]
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,3,4,5,7,8,9,6] => [[1,3,4,5,6,8,9],[2,7],[10]]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => [[1,2,3,4,5,7,8,9],[6],[10]]
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [4,1,3,2,10,5,6,8,9,7] => [[1,2,5,6,7,9],[3,8],[4,10]]
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,10,5,6,8,9,7] => [[1,3,5,6,7,9],[2,4,8],[10]]
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,6,3,5,4,10,7,9,8] => [[1,3,4,7,8],[2,5,9],[6,10]]
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [6,1,2,4,5,3,10,7,9,8] => [[1,2,3,5,7,8],[4,9],[6,10]]
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [4,1,3,2,6,5,10,7,9,8] => [[1,2,5,7,8],[3,6,9],[4,10]]
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,10,7,9,8] => [[1,3,5,7,8],[2,4,6,9],[10]]
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,8,9,10,7] => [[1,3,5,7,9,10],[2,4,6,8]]
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7] => [[1,3,4,5,7,9,10],[2,6,8]]
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [4,3,5,6,1,2,8,9,10,7] => [[1,2,6,7,9,10],[3,5,8],[4]]
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7] => [[1,3,5,6,7,9,10],[2,4,8]]
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7] => [[1,3,4,5,6,7,9,10],[2,8]]
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [6,3,4,5,7,8,9,10,1,2] => [[1,2,5,7,8,9,10],[3,4],[6]]
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [2,1,6,5,7,8,9,10,3,4] => [[1,3,4,8,9,10],[2,5,7],[6]]
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [2,5,4,6,7,8,9,1,10,3] => [[1,3,6,7,8,9,10],[2,4],[5]]
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,5] => [[1,3,5,7,8,9,10],[2,4,6]]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5] => [[1,3,4,5,7,8,9,10],[2,6]]
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,1,2] => [[1,2,6,7,8,9,10],[3,5],[4]]
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3] => [[1,3,5,6,7,8,9,10],[2,4]]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2]]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1] => [[1,3,4,5,6,7,8,9,10,11,12],[2]]
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,4,5,6,7,8,9,10,3,12,11] => [[1,3,5,6,7,8,9,10,11],[2,4,12]]
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,10,5,6,7,8,9,11,12,3,4] => [[1,3,4,7,8,9,11,12],[2,5,6],[10]]
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [4,3,5,6,7,8,9,10,1,2,12,11] => [[1,2,6,7,8,9,10,11],[3,5,12],[4]]
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,6,7,8,5,10,9,12,11] => [[1,3,5,7,8,9,11],[2,4,6,10,12]]
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,4,9,6,7,8,10,11,3,12,5] => [[1,3,5,7,8,10,11,12],[2,4,6],[9]]
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [2,3,4,1,6,7,8,5,10,9,12,11] => [[1,3,4,5,7,8,9,11],[2,6,10,12]]
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,6,7,8,5,10,11,12,9] => [[1,3,5,7,8,9,11,12],[2,4,6,10]]
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [2,5,4,6,7,8,9,1,10,3,12,11] => [[1,3,6,7,8,9,10,11],[2,4,12],[5]]
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [2,3,4,1,6,7,8,5,10,11,12,9] => [[1,3,4,5,7,8,9,11,12],[2,6,10]]
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,1,4,3,8,7,9,10,5,6,12,11] => [[1,3,5,6,10,11],[2,4,7,9,12],[8]]
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,4,5,8,7,9,10,3,11,12,6] => [[1,3,5,6,9,10,11,12],[2,4,7],[8]]
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [2,3,4,1,8,7,9,10,5,6,12,11] => [[1,3,4,5,6,10,11],[2,7,9,12],[8]]
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,6,5,7,8,3,4,10,9,12,11] => [[1,3,4,8,9,11],[2,5,7,10,12],[6]]
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,6,5,7,8,3,4,10,11,12,9] => [[1,3,4,8,9,11,12],[2,5,7,10],[6]]
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [2,3,6,5,7,8,1,9,10,4,12,11] => [[1,3,4,7,8,9,10,11],[2,5,12],[6]]
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,1,4,3,8,7,9,10,11,12,5,6] => [[1,3,5,6,10,11,12],[2,4,7,9],[8]]
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [6,3,4,5,7,8,1,2,10,9,12,11] => [[1,2,5,7,8,9,11],[3,4,10,12],[6]]
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [2,3,4,1,8,7,9,10,11,12,5,6] => [[1,3,4,5,6,10,11,12],[2,7,9],[8]]
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [6,3,4,5,7,8,1,2,10,11,12,9] => [[1,2,5,7,8,9,11,12],[3,4,10],[6]]
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [2,3,4,7,6,8,9,1,10,11,12,5] => [[1,3,4,5,8,9,10,11,12],[2,6],[7]]
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,4,7,6,8,9,3,10,5,12,11] => [[1,3,5,8,9,10,11],[2,4,6,12],[7]]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]]
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [2,3,4,1,6,5,8,7,10,9,12,11] => [[1,3,4,5,7,9,11],[2,6,8,10,12]]
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,10,11,12,9] => [[1,3,5,7,9,11,12],[2,4,6,8,10]]
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [2,3,4,1,6,5,8,7,10,11,12,9] => [[1,3,4,5,7,9,11,12],[2,6,8,10]]
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [2,3,6,5,7,8,9,10,1,11,12,4] => [[1,3,4,7,8,9,10,11,12],[2,5],[6]]
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,6,5,7,8,9,10,3,4,12,11] => [[1,3,4,8,9,10,11],[2,5,7,12],[6]]
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [2,5,4,6,7,8,9,10,11,1,12,3] => [[1,3,6,7,8,9,10,11,12],[2,4],[5]]
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,6,7,8,9,10,5,12,11] => [[1,3,5,7,8,9,10,11],[2,4,6,12]]
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,11,12,1,2] => [[1,2,6,7,8,9,10,11,12],[3,5],[4]]
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3] => [[1,3,5,6,7,8,9,10,11,12],[2,4]]
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [2,3,4,1,6,7,8,9,10,5,12,11] => [[1,3,4,5,7,8,9,10,11],[2,6,12]]
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,1,4,3,10,7,8,9,11,12,5,6] => [[1,3,5,6,9,11,12],[2,4,7,8],[10]]
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [6,3,4,5,7,8,9,10,1,2,12,11] => [[1,2,5,7,8,9,10,11],[3,4,12],[6]]
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [2,3,4,1,10,7,8,9,11,12,5,6] => [[1,3,4,5,6,9,11,12],[2,7,8],[10]]
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,4,5,6,3,8,7,10,9,12,11] => [[1,3,5,6,7,9,11],[2,4,8,10,12]]
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [4,3,5,6,1,2,8,7,10,9,12,11] => [[1,2,6,7,9,11],[3,5,8,10,12],[4]]
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,4,5,6,3,8,7,10,11,12,9] => [[1,3,5,6,7,9,11,12],[2,4,8,10]]
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [2,7,4,5,6,8,9,1,10,3,12,11] => [[1,3,5,6,8,9,10,11],[2,4,12],[7]]
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [4,3,5,6,1,2,8,7,10,11,12,9] => [[1,2,6,7,9,11,12],[3,5,8,10],[4]]
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,6,9,8,10,11,5,12,7] => [[1,3,5,7,10,11,12],[2,4,6,8],[9]]
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [2,3,4,5,6,1,8,7,10,9,12,11] => [[1,3,4,5,6,7,9,11],[2,8,10,12]]
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [2,3,4,1,6,9,8,10,11,5,12,7] => [[1,3,4,5,7,10,11,12],[2,6,8],[9]]
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [2,3,4,5,6,1,8,7,10,11,12,9] => [[1,3,4,5,6,7,9,11,12],[2,8,10]]
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [2,3,8,5,6,7,9,10,1,11,12,4] => [[1,3,4,6,7,9,10,11,12],[2,5],[8]]
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,8,5,6,7,9,10,3,4,12,11] => [[1,3,4,7,9,10,11],[2,5,6,12],[8]]
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,8,9,10,7,12,11] => [[1,3,5,7,9,10,11],[2,4,6,8,12]]
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [4,3,7,8,6,9,10,12,11,5,1,2] => [[1,2,8,9,10,11],[3,5,12],[4,6],[7]]
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,4,7,6,8,9,10,11,3,12,5] => [[1,3,5,8,9,10,11,12],[2,4,6],[7]]
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [2,3,4,1,6,5,8,9,10,7,12,11] => [[1,3,4,5,7,9,10,11],[2,6,8,12]]
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,1,4,3,6,5,10,9,11,12,7,8] => [[1,3,5,7,8,12],[2,4,6,9,11],[10]]
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [2,3,4,1,6,5,10,9,11,12,7,8] => [[1,3,4,5,7,8,12],[2,6,9,11],[10]]
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [2,9,4,5,6,7,8,10,11,1,12,3] => [[1,3,5,6,7,8,10,11,12],[2,4],[9]]
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,4,5,6,7,8,3,10,9,12,11] => [[1,3,5,6,7,8,9,11],[2,4,10,12]]
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,8,5,6,7,9,10,11,12,3,4] => [[1,3,4,7,9,10,11,12],[2,5,6],[8]]
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [4,3,5,6,7,8,1,2,10,9,12,11] => [[1,2,6,7,8,9,11],[3,5,10,12],[4]]
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [10,3,4,5,6,7,8,9,11,12,1,2] => [[1,2,5,6,7,8,9,11,12],[3,4],[10]]
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,4,5,6,7,8,3,10,11,12,9] => [[1,3,5,6,7,8,9,11,12],[2,4,10]]
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11] => [[1,3,4,5,6,7,8,9,10,11],[2,12]]
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [4,3,5,6,7,8,1,2,10,11,12,9] => [[1,2,6,7,8,9,11,12],[3,5,10],[4]]
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,8,9,10,11,12,7] => [[1,3,5,7,9,10,11,12],[2,4,6,8]]
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [2,5,4,6,7,1,8,3,10,9,12,11] => [[1,3,6,7,8,9,11],[2,4,10,12],[5]]
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [2,3,4,1,6,5,8,9,10,11,12,7] => [[1,3,4,5,7,9,10,11,12],[2,6,8]]
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [2,5,4,6,7,1,8,3,10,11,12,9] => [[1,3,6,7,8,9,11,12],[2,4,10],[5]]
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [2,7,4,5,6,8,9,10,11,1,12,3] => [[1,3,5,6,8,9,10,11,12],[2,4],[7]]
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,4,5,6,3,8,9,10,7,12,11] => [[1,3,5,6,7,9,10,11],[2,4,8,12]]
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,6,5,7,8,9,10,11,12,3,4] => [[1,3,4,8,9,10,11,12],[2,5,7],[6]]
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [4,3,5,6,1,2,8,9,10,7,12,11] => [[1,2,6,7,9,10,11],[3,5,8,12],[4]]
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,4,5,6,3,10,9,11,12,7,8] => [[1,3,5,6,7,8,12],[2,4,9,11],[10]]
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [8,3,4,5,6,7,9,10,1,2,12,11] => [[1,2,5,6,7,9,10,11],[3,4,12],[8]]
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [4,3,5,6,1,2,10,9,11,12,7,8] => [[1,2,6,7,8,12],[3,5,9,11],[4,10]]
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [6,3,4,5,7,8,9,10,11,12,1,2] => [[1,2,5,7,8,9,10,11,12],[3,4],[6]]
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,11,12,5] => [[1,3,5,7,8,9,10,11,12],[2,4,6]]
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [2,3,4,5,6,1,8,9,10,7,12,11] => [[1,3,4,5,6,7,9,10,11],[2,8,12]]
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,11,12,5] => [[1,3,4,5,7,8,9,10,11,12],[2,6]]
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [2,3,4,5,6,1,10,9,11,12,7,8] => [[1,3,4,5,6,7,8,12],[2,9,11],[10]]
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [8,3,4,5,6,7,9,10,11,12,1,2] => [[1,2,5,6,7,9,10,11,12],[3,4],[8]]
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,4,5,6,3,8,9,10,11,12,7] => [[1,3,5,6,7,9,10,11,12],[2,4,8]]
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [2,3,4,5,6,7,8,1,10,9,12,11] => [[1,3,4,5,6,7,8,9,11],[2,10,12]]
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [4,3,5,6,1,2,8,9,10,11,12,7] => [[1,2,6,7,9,10,11,12],[3,5,8],[4]]
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [2,3,4,5,6,7,8,1,10,11,12,9] => [[1,3,4,5,6,7,8,9,11,12],[2,10]]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [2,3,4,5,6,1,8,9,10,11,12,7] => [[1,3,4,5,6,7,9,10,11,12],[2,8]]
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,12,9,11,10] => [[1,3,5,7,9,10],[2,4,6,8,11],[12]]
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,10,7,9,8,12,11] => [[1,3,5,7,8,11],[2,4,6,9,12],[10]]
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,12,7,8,10,11,9] => [[1,3,5,7,8,9,11],[2,4,6,10],[12]]
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,8,5,7,6,10,9,12,11] => [[1,3,5,6,9,11],[2,4,7,10,12],[8]]
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,8,5,7,6,12,9,11,10] => [[1,3,5,6,9,10],[2,4,7,11],[8,12]]
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,10,5,6,8,9,7,12,11] => [[1,3,5,6,7,9,11],[2,4,8,12],[10]]
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,12,5,6,7,9,10,11,8] => [[1,3,5,6,7,8,10,11],[2,4,9],[12]]
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,6,3,5,4,8,7,10,9,12,11] => [[1,3,4,7,9,11],[2,5,8,10,12],[6]]
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,6,3,5,4,8,7,12,9,11,10] => [[1,3,4,7,9,10],[2,5,8,11],[6,12]]
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,3,5,4,10,7,9,8,12,11] => [[1,3,4,7,8,11],[2,5,9,12],[6,10]]
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,6,3,5,4,12,7,8,10,11,9] => [[1,3,4,7,8,9,11],[2,5,10],[6,12]]
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,8,3,4,6,7,5,10,9,12,11] => [[1,3,4,5,7,9,11],[2,6,10,12],[8]]
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,8,3,4,6,7,5,12,9,11,10] => [[1,3,4,5,7,9,10],[2,6,11],[8,12]]
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,10,3,4,5,7,8,9,6,12,11] => [[1,3,4,5,6,8,9,11],[2,7,12],[10]]
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,12,3,4,5,6,8,9,10,11,7] => [[1,3,4,5,6,7,9,10,11],[2,8],[12]]
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [4,1,3,2,6,5,8,7,10,9,12,11] => [[1,2,5,7,9,11],[3,6,8,10,12],[4]]
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [4,1,3,2,6,5,8,7,12,9,11,10] => [[1,2,5,7,9,10],[3,6,8,11],[4,12]]
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [4,1,3,2,6,5,10,7,9,8,12,11] => [[1,2,5,7,8,11],[3,6,9,12],[4,10]]
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [4,1,3,2,6,5,12,7,8,10,11,9] => [[1,2,5,7,8,9,11],[3,6,10],[4,12]]
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [4,1,3,2,8,5,7,6,10,9,12,11] => [[1,2,5,6,9,11],[3,7,10,12],[4,8]]
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [4,1,3,2,8,5,7,6,12,9,11,10] => [[1,2,5,6,9,10],[3,7,11],[4,8,12]]
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [4,1,3,2,10,5,6,8,9,7,12,11] => [[1,2,5,6,7,9,11],[3,8,12],[4,10]]
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [4,1,3,2,12,5,6,7,9,10,11,8] => [[1,2,5,6,7,8,10,11],[3,9],[4,12]]
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [6,1,2,4,5,3,8,7,10,9,12,11] => [[1,2,3,5,7,9,11],[4,8,10,12],[6]]
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [6,1,2,4,5,3,8,7,12,9,11,10] => [[1,2,3,5,7,9,10],[4,8,11],[6,12]]
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [6,1,2,4,5,3,10,7,9,8,12,11] => [[1,2,3,5,7,8,11],[4,9,12],[6,10]]
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [6,1,2,4,5,3,12,7,8,10,11,9] => [[1,2,3,5,7,8,9,11],[4,10],[6,12]]
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [8,1,2,3,5,6,7,4,10,9,12,11] => [[1,2,3,4,6,7,9,11],[5,10,12],[8]]
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [8,1,2,3,5,6,7,4,12,9,11,10] => [[1,2,3,4,6,7,9,10],[5,11],[8,12]]
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [10,1,2,3,4,6,7,8,9,5,12,11] => [[1,2,3,4,5,7,8,9,11],[6,12],[10]]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,1,2,3,4,5,7,8,9,10,11,6] => [[1,2,3,4,5,6,8,9,10,11],[7],[12]]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
This map is similar to Mp00235descent views to invisible inversion bottoms, but different beginning with permutations of six elements.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
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.