Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Images
[(1,2)] => [2,1] => [[1],[2]]
[(1,2),(3,4)] => [2,1,4,3] => [[1,3],[2,4]]
[(1,3),(2,4)] => [3,4,1,2] => [[1,2],[3,4]]
[(1,4),(2,3)] => [4,3,2,1] => [[1],[2],[3],[4]]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [[1,2,5],[3,4,6]]
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]]
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [[1,4],[2,6],[3],[5]]
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [[1,4],[2,5],[3],[6]]
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [[1,3],[2,5],[4],[6]]
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [[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),(3,5),(4,6)] => [2,1,5,6,3,4] => [[1,3,4],[2,5,6]]
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]]
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [[1,2],[3,4],[5],[6]]
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [[1,2],[3,5],[4],[6]]
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]]
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]]
[(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),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]]
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]]
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [[1,4,7],[2,6,8],[3],[5]]
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [[1,4,7],[2,5,8],[3],[6]]
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [[1,4,6],[2,5,8],[3],[7]]
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [[1,4,6],[2,5,7],[3],[8]]
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [[1,3,6],[2,5,7],[4],[8]]
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [[1,3,6],[2,5,8],[4],[7]]
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [[1,3,7],[2,5,8],[4],[6]]
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [[1,3,7],[2,6,8],[4],[5]]
[(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),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]]
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [[1,2,7],[3,4,8],[5],[6]]
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [[1,2,7],[3,5,8],[4],[6]]
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [[1,2,7],[3,6,8],[4],[5]]
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]]
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [[1,6],[2,8],[3],[4],[5],[7]]
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [[1,6],[2,7],[3],[4],[5],[8]]
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [[1,5],[2,7],[3],[4],[6],[8]]
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [[1,5],[2,8],[3],[4],[6],[7]]
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [[1,2,5],[3,7,8],[4],[6]]
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [[1,2,6],[3,7,8],[4],[5]]
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [[1,2,6],[3,5,8],[4],[7]]
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [[1,2,6],[3,4,8],[5],[7]]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [[1,3,6],[2,4,8],[5],[7]]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [[1,3,6],[2,4,7],[5],[8]]
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [[1,2,6],[3,4,7],[5],[8]]
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [[1,2,6],[3,5,7],[4],[8]]
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [[1,2],[3,6],[4,7],[5,8]]
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [[1,2],[3,5],[4,7],[6,8]]
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [[1,2],[3,5],[4,6],[7,8]]
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [[1,5],[2,6],[3],[4],[7],[8]]
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [[1,4],[2,6],[3],[5],[7],[8]]
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8]]
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [[1,2],[3,4],[5,7],[6,8]]
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [[1,2,4],[3,6,7],[5],[8]]
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [[1,2,5],[3,6,7],[4],[8]]
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [[1,2,5],[3,4,7],[6],[8]]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [[1,3,5],[2,4,7],[6],[8]]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [[1,3,5],[2,4,8],[6],[7]]
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [[1,2,5],[3,4,8],[6],[7]]
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [[1,2,5],[3,6,8],[4],[7]]
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [[1,2,4],[3,6,8],[5],[7]]
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [[1,2,4],[3,7,8],[5],[6]]
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]]
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]]
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [[1,3,4],[2,6,7],[5],[8]]
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]]
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [[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),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [[1,3,4,5],[2,6,7,8]]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [[1,3,4,6],[2,5,7,8]]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [[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]]
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [[1,3,6],[2,7,8],[4],[5]]
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [[1,3,5],[2,7,8],[4],[6]]
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [[1,3,5],[2,6,8],[4],[7]]
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [[1,3,5],[2,6,7],[4],[8]]
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [[1,4,5],[2,6,7],[3],[8]]
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [[1,4,5],[2,6,8],[3],[7]]
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [[1,4,5],[2,7,8],[3],[6]]
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [[1,4,6],[2,7,8],[3],[5]]
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [[1,5,6],[2,7,8],[3],[4]]
[(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),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [[1,3,5,6],[2,4,7,8]]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [[1,2,5],[3,4,6],[7],[8]]
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]]
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [[1,4],[2,6],[3,7],[5,8]]
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [[1,4],[2,5],[3,7],[6,8]]
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [[1,4],[2,5],[3,6],[7,8]]
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [[1,4],[2,5],[3],[6],[7],[8]]
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [[1,3],[2,5],[4],[6],[7],[8]]
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [[1,3],[2,5],[4,6],[7,8]]
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [[1,3],[2,5],[4,7],[6,8]]
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [[1,3],[2,6],[4,7],[5,8]]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [[1,2,3],[4,5,6],[7],[8]]
>>> Load all 149 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [[1,2,4],[3,5,6],[7],[8]]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [[1,3,4],[2,5,6],[7],[8]]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [[1,3,4],[2,5,7],[6],[8]]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [[1,2,4],[3,5,7],[6],[8]]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [[1,2,3],[4,5,7],[6],[8]]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [[1,2,3],[4,6,7],[5],[8]]
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [[1,3],[2,4],[5,7],[6,8]]
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [[1,3],[2,4],[5,6],[7,8]]
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [[1,3],[2,6],[4],[5],[7],[8]]
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]]
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]]
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [[1,2,3],[4,7,8],[5],[6]]
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [[1,2,3],[4,6,8],[5],[7]]
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [[1,2,3],[4,5,8],[6],[7]]
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [[1,2,4],[3,5,8],[6],[7]]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [[1,3,4],[2,5,8],[6],[7]]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]]
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [[1,2],[3,4],[5],[6],[7],[8]]
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [[1,2],[3,5],[4],[6],[7],[8]]
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [[1,2],[3,6],[4],[5],[7],[8]]
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [[1,2],[3,7],[4],[5],[6],[8]]
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]]
[(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),(9,10)] => [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] => [[1,2,5,7,9],[3,4,6,8,10]]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [[1,5,7,9],[2,6,8,10],[3],[4]]
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [[1,7,9],[2,8,10],[3],[4],[5],[6]]
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => [[1,2,7],[3,4,10],[5,6],[8,9]]
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [[1,5,9],[2,6,10],[3,7],[4,8]]
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]]
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]]
[(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]]
[(1,6),(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]]
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => [[1,4,5,6],[2,8,9,10],[3],[7]]
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => [[1,6,7],[2,9,10],[3],[4],[5],[8]]
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [[1,3,5,7],[2,4,6,8],[9],[10]]
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [[1,3,7],[2,4,8],[5,9],[6,10]]
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5],[6]]
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [[1,4],[2,6],[3,8],[5,10],[7],[9]]
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8],[9],[10]]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]]
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]]
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [9,10,8,7,6,5,4,3,1,2] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]]
[(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]]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
[(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]]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
[(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]]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the 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.