Identifier
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Images
[(1,2)] => [2,1] => [2,1] => [2]
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [2,2]
[(1,3),(2,4)] => [3,4,1,2] => [4,3,2,1] => [1,2,1]
[(1,4),(2,3)] => [3,4,2,1] => [4,3,1,2] => [1,3]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,2,2]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,3,2,1,6,5] => [1,2,1,2]
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [4,3,1,2,6,5] => [1,3,2]
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [6,3,1,5,4,2] => [1,2,2,1]
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [6,3,1,5,2,4] => [1,2,3]
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [6,5,4,2,1,3] => [1,1,2,2]
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [6,5,4,2,3,1] => [1,1,3,1]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => [1,1,2,1,1]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [6,3,2,5,4,1] => [1,2,2,1]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => [2,1,2,1]
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [2,1,6,5,3,4] => [2,1,3]
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [6,3,2,5,1,4] => [1,2,3]
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [6,5,4,3,1,2] => [1,1,2,2]
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [6,5,4,1,3,2] => [1,1,3,1]
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => [1,1,4]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,2,2,2]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [4,3,2,1,6,5,8,7] => [1,2,1,2,2]
[(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [4,3,1,2,6,5,8,7] => [1,3,2,2]
[(1,5),(2,3),(4,6),(7,8)] => [3,5,2,6,1,4,8,7] => [6,3,1,5,4,2,8,7] => [1,2,2,1,2]
[(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [6,3,1,5,2,4,8,7] => [1,2,3,2]
[(1,7),(2,3),(4,5),(6,8)] => [3,5,2,7,4,8,1,6] => [8,3,1,5,2,7,6,4] => [1,2,2,2,1]
[(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [8,3,1,5,2,7,4,6] => [1,2,2,3]
[(1,8),(2,4),(3,5),(6,7)] => [4,5,7,2,3,8,6,1] => [8,5,4,2,1,7,3,6] => [1,1,2,1,3]
[(1,7),(2,4),(3,5),(6,8)] => [4,5,7,2,3,8,1,6] => [8,5,4,2,1,7,6,3] => [1,1,2,1,2,1]
[(1,6),(2,4),(3,5),(7,8)] => [4,5,6,2,3,1,8,7] => [6,5,4,2,1,3,8,7] => [1,1,2,2,2]
[(1,5),(2,4),(3,6),(7,8)] => [4,5,6,2,1,3,8,7] => [6,5,4,2,3,1,8,7] => [1,1,3,1,2]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [6,5,4,3,2,1,8,7] => [1,1,2,1,1,2]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [6,3,2,5,4,1,8,7] => [1,2,2,1,2]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,6,5,4,3,8,7] => [2,1,2,1,2]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [2,1,6,5,3,4,8,7] => [2,1,3,2]
[(1,3),(2,6),(4,5),(7,8)] => [3,5,1,6,4,2,8,7] => [6,3,2,5,1,4,8,7] => [1,2,3,2]
[(1,4),(2,6),(3,5),(7,8)] => [4,5,6,1,3,2,8,7] => [6,5,4,3,1,2,8,7] => [1,1,2,2,2]
[(1,5),(2,6),(3,4),(7,8)] => [4,5,6,3,1,2,8,7] => [6,5,4,1,3,2,8,7] => [1,1,3,1,2]
[(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [6,5,4,1,2,3,8,7] => [1,1,4,2]
[(1,7),(2,5),(3,4),(6,8)] => [4,5,7,3,2,8,1,6] => [8,5,4,1,2,7,6,3] => [1,1,3,2,1]
[(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [8,5,4,1,2,7,3,6] => [1,1,3,3]
[(1,8),(2,6),(3,4),(5,7)] => [4,6,7,3,8,2,5,1] => [8,7,4,1,6,3,2,5] => [1,1,2,2,2]
[(1,7),(2,6),(3,4),(5,8)] => [4,6,7,3,8,2,1,5] => [8,7,4,1,6,3,5,2] => [1,1,2,3,1]
[(1,6),(2,7),(3,4),(5,8)] => [4,6,7,3,8,1,2,5] => [8,7,4,1,6,5,3,2] => [1,1,2,2,1,1]
[(1,5),(2,7),(3,4),(6,8)] => [4,5,7,3,1,8,2,6] => [8,5,4,1,3,7,6,2] => [1,1,3,2,1]
[(1,4),(2,7),(3,5),(6,8)] => [4,5,7,1,3,8,2,6] => [8,5,4,3,1,7,6,2] => [1,1,2,1,2,1]
[(1,3),(2,7),(4,5),(6,8)] => [3,5,1,7,4,8,2,6] => [8,3,2,5,1,7,6,4] => [1,2,2,2,1]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,5,7,4,8,3,6] => [2,1,8,5,3,7,6,4] => [2,1,2,2,1]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [2,1,8,5,3,7,4,6] => [2,1,2,3]
[(1,3),(2,8),(4,5),(6,7)] => [3,5,1,7,4,8,6,2] => [8,3,2,5,1,7,4,6] => [1,2,2,3]
[(1,4),(2,8),(3,5),(6,7)] => [4,5,7,1,3,8,6,2] => [8,5,4,3,1,7,2,6] => [1,1,2,1,3]
[(1,5),(2,8),(3,4),(6,7)] => [4,5,7,3,1,8,6,2] => [8,5,4,1,3,7,2,6] => [1,1,3,3]
[(1,6),(2,8),(3,4),(5,7)] => [4,6,7,3,8,1,5,2] => [8,7,4,1,6,5,2,3] => [1,1,2,2,2]
[(1,7),(2,8),(3,4),(5,6)] => [4,6,7,3,8,5,1,2] => [8,7,4,1,6,2,5,3] => [1,1,2,3,1]
[(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [8,7,4,1,6,2,3,5] => [1,1,2,4]
[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => [8,7,6,5,2,1,3,4] => [1,1,1,2,3]
[(1,7),(2,8),(3,5),(4,6)] => [5,6,7,8,3,4,1,2] => [8,7,6,5,2,1,4,3] => [1,1,1,2,2,1]
[(1,6),(2,8),(3,5),(4,7)] => [5,6,7,8,3,1,4,2] => [8,7,6,5,2,4,1,3] => [1,1,1,3,2]
[(1,5),(2,8),(3,6),(4,7)] => [5,6,7,8,1,3,4,2] => [8,7,6,5,4,2,1,3] => [1,1,1,2,1,2]
[(1,4),(2,8),(3,6),(5,7)] => [4,6,7,1,8,3,5,2] => [8,7,4,3,6,2,1,5] => [1,1,2,2,2]
[(1,3),(2,8),(4,6),(5,7)] => [3,6,1,7,8,4,5,2] => [8,3,2,7,6,4,1,5] => [1,2,1,2,2]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,6,7,8,4,5,3] => [2,1,8,7,6,4,3,5] => [2,1,1,2,2]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,6,7,8,4,3,5] => [2,1,8,7,6,4,5,3] => [2,1,1,3,1]
[(1,3),(2,7),(4,6),(5,8)] => [3,6,1,7,8,4,2,5] => [8,3,2,7,6,4,5,1] => [1,2,1,3,1]
[(1,4),(2,7),(3,6),(5,8)] => [4,6,7,1,8,3,2,5] => [8,7,4,3,6,2,5,1] => [1,1,2,3,1]
[(1,5),(2,7),(3,6),(4,8)] => [5,6,7,8,1,3,2,4] => [8,7,6,5,4,2,3,1] => [1,1,1,2,2,1]
[(1,6),(2,7),(3,5),(4,8)] => [5,6,7,8,3,1,2,4] => [8,7,6,5,2,4,3,1] => [1,1,1,3,1,1]
[(1,7),(2,6),(3,5),(4,8)] => [5,6,7,8,3,2,1,4] => [8,7,6,5,2,3,4,1] => [1,1,1,4,1]
[(1,8),(2,6),(3,5),(4,7)] => [5,6,7,8,3,2,4,1] => [8,7,6,5,2,3,1,4] => [1,1,1,3,2]
[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => [8,7,6,5,3,2,1,4] => [1,1,1,2,1,2]
[(1,7),(2,5),(3,6),(4,8)] => [5,6,7,8,2,3,1,4] => [8,7,6,5,3,2,4,1] => [1,1,1,2,2,1]
[(1,6),(2,5),(3,7),(4,8)] => [5,6,7,8,2,1,3,4] => [8,7,6,5,3,4,2,1] => [1,1,1,3,1,1]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [8,7,6,5,4,3,2,1] => [1,1,1,2,1,1,1]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [8,7,4,3,6,5,2,1] => [1,1,2,2,1,1]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [8,3,2,7,6,5,4,1] => [1,2,1,2,1,1]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,8,7,6,5,4,3] => [2,1,1,2,1,1]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,8,5,4,7,6,3] => [2,1,2,2,1]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [8,3,2,5,4,7,6,1] => [1,2,2,2,1]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [8,5,4,3,2,7,6,1] => [1,1,2,1,2,1]
[(1,5),(2,4),(3,7),(6,8)] => [4,5,7,2,1,8,3,6] => [8,5,4,2,3,7,6,1] => [1,1,3,2,1]
[(1,6),(2,4),(3,7),(5,8)] => [4,6,7,2,8,1,3,5] => [8,7,4,2,6,5,3,1] => [1,1,2,2,1,1]
[(1,7),(2,4),(3,6),(5,8)] => [4,6,7,2,8,3,1,5] => [8,7,4,2,6,3,5,1] => [1,1,2,3,1]
[(1,8),(2,4),(3,6),(5,7)] => [4,6,7,2,8,3,5,1] => [8,7,4,2,6,3,1,5] => [1,1,2,2,2]
[(1,8),(2,3),(4,6),(5,7)] => [3,6,2,7,8,4,5,1] => [8,3,1,7,6,4,2,5] => [1,2,1,2,2]
[(1,7),(2,3),(4,6),(5,8)] => [3,6,2,7,8,4,1,5] => [8,3,1,7,6,4,5,2] => [1,2,1,3,1]
[(1,6),(2,3),(4,7),(5,8)] => [3,6,2,7,8,1,4,5] => [8,3,1,7,6,5,4,2] => [1,2,1,2,1,1]
[(1,5),(2,3),(4,7),(6,8)] => [3,5,2,7,1,8,4,6] => [8,3,1,5,4,7,6,2] => [1,2,2,2,1]
[(1,4),(2,3),(5,7),(6,8)] => [3,4,2,1,7,8,5,6] => [4,3,1,2,8,7,6,5] => [1,3,1,2,1]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [4,3,2,1,8,7,6,5] => [1,2,1,1,2,1]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,7,6,5] => [2,2,1,2,1]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,7,5,6] => [2,2,1,3]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,7,8,6,5] => [4,3,2,1,8,7,5,6] => [1,2,1,1,3]
[(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [4,3,1,2,8,7,5,6] => [1,3,1,3]
[(1,5),(2,3),(4,8),(6,7)] => [3,5,2,7,1,8,6,4] => [8,3,1,5,4,7,2,6] => [1,2,2,3]
[(1,6),(2,3),(4,8),(5,7)] => [3,6,2,7,8,1,5,4] => [8,3,1,7,6,5,2,4] => [1,2,1,2,2]
[(1,7),(2,3),(4,8),(5,6)] => [3,6,2,7,8,5,1,4] => [8,3,1,7,6,2,5,4] => [1,2,1,3,1]
[(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [8,3,1,7,6,2,4,5] => [1,2,1,4]
[(1,8),(2,4),(3,7),(5,6)] => [4,6,7,2,8,5,3,1] => [8,7,4,2,6,1,3,5] => [1,1,2,4]
[(1,7),(2,4),(3,8),(5,6)] => [4,6,7,2,8,5,1,3] => [8,7,4,2,6,1,5,3] => [1,1,2,3,1]
[(1,6),(2,4),(3,8),(5,7)] => [4,6,7,2,8,1,5,3] => [8,7,4,2,6,5,1,3] => [1,1,2,2,2]
[(1,5),(2,4),(3,8),(6,7)] => [4,5,7,2,1,8,6,3] => [8,5,4,2,3,7,1,6] => [1,1,3,3]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,7,1,2,8,6,3] => [8,5,4,3,2,7,1,6] => [1,1,2,1,3]
>>> Load all 300 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,7,2,8,6,4] => [8,3,2,5,4,7,1,6] => [1,2,2,3]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,7,3,8,6,4] => [2,1,8,5,4,7,3,6] => [2,1,2,3]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,7,8,3,5,4] => [2,1,8,7,6,5,3,4] => [2,1,1,2,2]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,7,8,2,5,4] => [8,3,2,7,6,5,1,4] => [1,2,1,2,2]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,7,1,8,2,5,3] => [8,7,4,3,6,5,1,2] => [1,1,2,2,2]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,7,8,1,2,4,3] => [8,7,6,5,4,3,1,2] => [1,1,1,2,1,2]
[(1,6),(2,5),(3,8),(4,7)] => [5,6,7,8,2,1,4,3] => [8,7,6,5,3,4,1,2] => [1,1,1,3,2]
[(1,7),(2,5),(3,8),(4,6)] => [5,6,7,8,2,4,1,3] => [8,7,6,5,3,1,4,2] => [1,1,1,2,2,1]
[(1,8),(2,5),(3,7),(4,6)] => [5,6,7,8,2,4,3,1] => [8,7,6,5,3,1,2,4] => [1,1,1,2,3]
[(1,8),(2,6),(3,7),(4,5)] => [5,6,7,8,4,2,3,1] => [8,7,6,5,1,3,2,4] => [1,1,1,3,2]
[(1,7),(2,6),(3,8),(4,5)] => [5,6,7,8,4,2,1,3] => [8,7,6,5,1,3,4,2] => [1,1,1,4,1]
[(1,6),(2,7),(3,8),(4,5)] => [5,6,7,8,4,1,2,3] => [8,7,6,5,1,4,3,2] => [1,1,1,3,1,1]
[(1,5),(2,7),(3,8),(4,6)] => [5,6,7,8,1,4,2,3] => [8,7,6,5,4,1,3,2] => [1,1,1,2,2,1]
[(1,4),(2,7),(3,8),(5,6)] => [4,6,7,1,8,5,2,3] => [8,7,4,3,6,1,5,2] => [1,1,2,3,1]
[(1,3),(2,7),(4,8),(5,6)] => [3,6,1,7,8,5,2,4] => [8,3,2,7,6,1,5,4] => [1,2,1,3,1]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,6,7,8,5,3,4] => [2,1,8,7,6,3,5,4] => [2,1,1,3,1]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [2,1,8,7,6,3,4,5] => [2,1,1,4]
[(1,3),(2,8),(4,7),(5,6)] => [3,6,1,7,8,5,4,2] => [8,3,2,7,6,1,4,5] => [1,2,1,4]
[(1,4),(2,8),(3,7),(5,6)] => [4,6,7,1,8,5,3,2] => [8,7,4,3,6,1,2,5] => [1,1,2,4]
[(1,5),(2,8),(3,7),(4,6)] => [5,6,7,8,1,4,3,2] => [8,7,6,5,4,1,2,3] => [1,1,1,2,3]
[(1,6),(2,8),(3,7),(4,5)] => [5,6,7,8,4,1,3,2] => [8,7,6,5,1,4,2,3] => [1,1,1,3,2]
[(1,7),(2,8),(3,6),(4,5)] => [5,6,7,8,4,3,1,2] => [8,7,6,5,1,2,4,3] => [1,1,1,4,1]
[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4] => [1,1,1,5]
[(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] => [2,2,2,2,2]
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [1,2,1,2,2,2]
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => [1,1,2,1,1,2,2]
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [3,5,1,6,2,4,8,7,10,9] => [6,3,2,5,4,1,8,7,10,9] => [1,2,2,1,2,2]
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => [2,1,2,1,2,2]
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [8,7,6,5,4,3,2,1,10,9] => [1,1,1,2,1,1,1,2]
[(1,4),(2,6),(3,7),(5,8),(9,10)] => [4,6,7,1,8,2,3,5,10,9] => [8,7,4,3,6,5,2,1,10,9] => [1,1,2,2,1,1,2]
[(1,3),(2,6),(4,7),(5,8),(9,10)] => [3,6,1,7,8,2,4,5,10,9] => [8,3,2,7,6,5,4,1,10,9] => [1,2,1,2,1,1,2]
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,8,7,6,5,4,3,10,9] => [2,1,1,2,1,1,2]
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [2,1,5,7,3,8,4,6,10,9] => [2,1,8,5,4,7,6,3,10,9] => [2,1,2,2,1,2]
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [3,5,1,7,2,8,4,6,10,9] => [8,3,2,5,4,7,6,1,10,9] => [1,2,2,2,1,2]
[(1,4),(2,5),(3,7),(6,8),(9,10)] => [4,5,7,1,2,8,3,6,10,9] => [8,5,4,3,2,7,6,1,10,9] => [1,1,2,1,2,1,2]
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [4,3,2,1,8,7,6,5,10,9] => [1,2,1,1,2,1,2]
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,8,7,6,5,10,9] => [2,2,1,2,1,2]
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,9,8,7,6,5,4,3] => [2,1,1,1,2,1,1,1]
[(1,3),(2,7),(4,8),(5,9),(6,10)] => [3,7,1,8,9,10,2,4,5,6] => [10,3,2,9,8,7,6,5,4,1] => [1,2,1,1,2,1,1,1]
[(1,4),(2,7),(3,8),(5,9),(6,10)] => [4,7,8,1,9,10,2,3,5,6] => [10,9,4,3,8,7,6,5,2,1] => [1,1,2,1,2,1,1,1]
[(1,5),(2,7),(3,8),(4,9),(6,10)] => [5,7,8,9,1,10,2,3,4,6] => [10,9,8,5,4,7,6,3,2,1] => [1,1,1,2,2,1,1,1]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,2,1,1,1,1]
[(1,5),(2,6),(3,8),(4,9),(7,10)] => [5,6,8,9,1,2,10,3,4,7] => [10,9,6,5,4,3,8,7,2,1] => [1,1,1,2,1,2,1,1]
[(1,4),(2,6),(3,8),(5,9),(7,10)] => [4,6,8,1,9,2,10,3,5,7] => [10,9,4,3,6,5,8,7,2,1] => [1,1,2,2,2,1,1]
[(1,3),(2,6),(4,8),(5,9),(7,10)] => [3,6,1,8,9,2,10,4,5,7] => [10,3,2,9,6,5,8,7,4,1] => [1,2,1,2,2,1,1]
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [2,1,6,8,9,3,10,4,5,7] => [2,1,10,9,6,5,8,7,4,3] => [2,1,1,2,2,1,1]
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [2,1,5,8,3,9,10,4,6,7] => [2,1,10,5,4,9,8,7,6,3] => [2,1,2,1,2,1,1]
[(1,3),(2,5),(4,8),(6,9),(7,10)] => [3,5,1,8,2,9,10,4,6,7] => [10,3,2,5,4,9,8,7,6,1] => [1,2,2,1,2,1,1]
[(1,4),(2,5),(3,8),(6,9),(7,10)] => [4,5,8,1,2,9,10,3,6,7] => [10,5,4,3,2,9,8,7,6,1] => [1,1,2,1,1,2,1,1]
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [4,3,2,1,10,9,8,7,6,5] => [1,2,1,1,1,2,1,1]
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,10,9,8,7,6,5] => [2,2,1,1,2,1,1]
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [2,1,4,3,7,9,5,10,6,8] => [2,1,4,3,10,7,6,9,8,5] => [2,2,1,2,2,1]
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [3,4,1,2,7,9,5,10,6,8] => [4,3,2,1,10,7,6,9,8,5] => [1,2,1,1,2,2,1]
[(1,4),(2,5),(3,7),(6,9),(8,10)] => [4,5,7,1,2,9,3,10,6,8] => [10,5,4,3,2,7,6,9,8,1] => [1,1,2,1,2,2,1]
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8] => [10,3,2,5,4,7,6,9,8,1] => [1,2,2,2,2,1]
[(1,2),(3,5),(4,7),(6,9),(8,10)] => [2,1,5,7,3,9,4,10,6,8] => [2,1,10,5,4,7,6,9,8,3] => [2,1,2,2,2,1]
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [2,1,6,7,9,3,4,10,5,8] => [2,1,10,7,6,5,4,9,8,3] => [2,1,1,2,1,2,1]
[(1,3),(2,6),(4,7),(5,9),(8,10)] => [3,6,1,7,9,2,4,10,5,8] => [10,3,2,7,6,5,4,9,8,1] => [1,2,1,2,1,2,1]
[(1,4),(2,6),(3,7),(5,9),(8,10)] => [4,6,7,1,9,2,3,10,5,8] => [10,7,4,3,6,5,2,9,8,1] => [1,1,2,2,1,2,1]
[(1,5),(2,6),(3,7),(4,9),(8,10)] => [5,6,7,9,1,2,3,10,4,8] => [10,7,6,5,4,3,2,9,8,1] => [1,1,1,2,1,1,2,1]
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,6,5,4,3,10,9,8,7] => [2,1,2,1,1,2,1]
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [3,5,1,6,2,4,9,10,7,8] => [6,3,2,5,4,1,10,9,8,7] => [1,2,2,1,1,2,1]
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [6,5,4,3,2,1,10,9,8,7] => [1,1,2,1,1,1,2,1]
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [4,3,2,1,6,5,10,9,8,7] => [1,2,1,2,1,2,1]
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,10,9,8,7] => [2,2,2,1,2,1]
[(1,6),(2,10),(3,9),(4,8),(5,7)] => [6,7,8,9,10,1,5,4,3,2] => [10,9,8,7,6,5,1,2,3,4] => [1,1,1,1,2,4]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [6,7,8,9,10,5,4,3,2,1] => [10,9,8,7,6,1,2,3,4,5] => [1,1,1,1,6]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2]
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,2,2,2,1,2,1]
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,2,2,1,2,1,2]
[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => [2,1,4,3,6,5,9,11,7,12,8,10] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,2,2,1,2,2,1]
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,2,2,1,1,2,1,1]
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,2,1,2,1,2,2]
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,2,1,2,1,1,2,1]
[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => [2,1,4,3,7,9,5,10,6,8,12,11] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,2,1,2,2,1,2]
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => [2,1,4,3,7,9,5,11,6,12,8,10] => [2,1,4,3,12,7,6,9,8,11,10,5] => [2,2,1,2,2,2,1]
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => [2,1,4,3,7,10,5,11,12,6,8,9] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,2,1,2,1,2,1,1]
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,2,1,1,2,1,1,2]
[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => [2,1,4,3,8,9,11,5,6,12,7,10] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,2,1,1,2,1,2,1]
[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => [2,1,4,3,8,10,11,5,12,6,7,9] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,2,1,1,2,2,1,1]
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,2,1,1,1,2,1,1,1]
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,2,1,2,2,2]
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,2,1,2,1,2,1]
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,2,1,1,2,1,2]
[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => [2,1,5,6,3,4,9,11,7,12,8,10] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,2,1,1,2,2,1]
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,2,1,1,1,2,1,1]
[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => [2,1,5,7,3,8,4,6,10,9,12,11] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,2,2,1,2,2]
[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => [2,1,5,7,3,8,4,6,11,12,9,10] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,2,2,1,1,2,1]
[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => [2,1,5,7,3,9,4,10,6,8,12,11] => [2,1,10,5,4,7,6,9,8,3,12,11] => [2,1,2,2,2,1,2]
[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => [2,1,5,7,3,9,4,11,6,12,8,10] => [2,1,12,5,4,7,6,9,8,11,10,3] => [2,1,2,2,2,2,1]
[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => [2,1,5,7,3,10,4,11,12,6,8,9] => [2,1,12,5,4,7,6,11,10,9,8,3] => [2,1,2,2,1,2,1,1]
[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => [2,1,5,8,3,9,10,4,6,7,12,11] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,2,1,2,1,1,2]
[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => [2,1,5,8,3,9,11,4,6,12,7,10] => [2,1,12,5,4,9,8,7,6,11,10,3] => [2,1,2,1,2,1,2,1]
[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => [2,1,5,8,3,10,11,4,12,6,7,9] => [2,1,12,5,4,11,8,7,10,9,6,3] => [2,1,2,1,2,2,1,1]
[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => [2,1,5,9,3,10,11,12,4,6,7,8] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,2,1,1,2,1,1,1]
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,1,2,1,1,2,2]
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,1,2,1,1,1,2,1]
[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => [2,1,6,7,9,3,4,10,5,8,12,11] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,1,2,1,2,1,2]
[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => [2,1,6,7,9,3,4,11,5,12,8,10] => [2,1,12,7,6,5,4,9,8,11,10,3] => [2,1,1,2,1,2,2,1]
[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => [2,1,6,7,10,3,4,11,12,5,8,9] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,1,2,1,1,2,1,1]
[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => [2,1,6,8,9,3,10,4,5,7,12,11] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,1,2,2,1,1,2]
[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => [2,1,6,8,9,3,11,4,5,12,7,10] => [2,1,12,9,6,5,8,7,4,11,10,3] => [2,1,1,2,2,1,2,1]
[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => [2,1,6,8,10,3,11,4,12,5,7,9] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,1,2,2,2,1,1]
[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => [2,1,6,9,10,3,11,12,4,5,7,8] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,1,2,1,2,1,1,1]
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,1,1,2,1,1,1,2]
[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => [2,1,7,8,9,11,3,4,5,12,6,10] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,1,1,2,1,1,2,1]
[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => [2,1,7,8,10,11,3,4,12,5,6,9] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,1,1,2,1,2,1,1]
[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => [2,1,7,9,10,11,3,12,4,5,6,8] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,1,1,2,2,1,1,1]
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,1,1,1,2,1,1,1,1]
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => [1,2,1,2,2,2,2]
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [4,3,2,1,6,5,8,7,12,11,10,9] => [1,2,1,2,2,1,2,1]
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => [1,2,1,2,1,2,1,2]
[(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => [3,4,1,2,6,5,9,11,7,12,8,10] => [4,3,2,1,6,5,12,9,8,11,10,7] => [1,2,1,2,1,2,2,1]
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [4,3,2,1,6,5,12,11,10,9,8,7] => [1,2,1,2,1,1,2,1,1]
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => [1,2,1,1,2,1,2,2]
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [4,3,2,1,8,7,6,5,12,11,10,9] => [1,2,1,1,2,1,1,2,1]
[(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => [3,4,1,2,7,9,5,10,6,8,12,11] => [4,3,2,1,10,7,6,9,8,5,12,11] => [1,2,1,1,2,2,1,2]
[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => [3,4,1,2,7,9,5,11,6,12,8,10] => [4,3,2,1,12,7,6,9,8,11,10,5] => [1,2,1,1,2,2,2,1]
[(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => [3,4,1,2,7,10,5,11,12,6,8,9] => [4,3,2,1,12,7,6,11,10,9,8,5] => [1,2,1,1,2,1,2,1,1]
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [4,3,2,1,10,9,8,7,6,5,12,11] => [1,2,1,1,1,2,1,1,2]
[(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => [3,4,1,2,8,9,11,5,6,12,7,10] => [4,3,2,1,12,9,8,7,6,11,10,5] => [1,2,1,1,1,2,1,2,1]
[(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => [3,4,1,2,8,10,11,5,12,6,7,9] => [4,3,2,1,12,11,8,7,10,9,6,5] => [1,2,1,1,1,2,2,1,1]
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [4,3,2,1,12,11,10,9,8,7,6,5] => [1,2,1,1,1,1,2,1,1,1]
[(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => [3,5,1,6,2,4,8,7,10,9,12,11] => [6,3,2,5,4,1,8,7,10,9,12,11] => [1,2,2,1,2,2,2]
[(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => [3,5,1,6,2,4,8,7,11,12,9,10] => [6,3,2,5,4,1,8,7,12,11,10,9] => [1,2,2,1,2,1,2,1]
[(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => [3,5,1,6,2,4,9,10,7,8,12,11] => [6,3,2,5,4,1,10,9,8,7,12,11] => [1,2,2,1,1,2,1,2]
[(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => [3,5,1,6,2,4,9,11,7,12,8,10] => [6,3,2,5,4,1,12,9,8,11,10,7] => [1,2,2,1,1,2,2,1]
[(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => [3,5,1,6,2,4,10,11,12,7,8,9] => [6,3,2,5,4,1,12,11,10,9,8,7] => [1,2,2,1,1,1,2,1,1]
[(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => [3,5,1,7,2,8,4,6,10,9,12,11] => [8,3,2,5,4,7,6,1,10,9,12,11] => [1,2,2,2,1,2,2]
[(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => [3,5,1,7,2,8,4,6,11,12,9,10] => [8,3,2,5,4,7,6,1,12,11,10,9] => [1,2,2,2,1,1,2,1]
[(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => [3,5,1,7,2,9,4,10,6,8,12,11] => [10,3,2,5,4,7,6,9,8,1,12,11] => [1,2,2,2,2,1,2]
[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => [3,5,1,7,2,9,4,11,6,12,8,10] => [12,3,2,5,4,7,6,9,8,11,10,1] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)] => [3,5,1,7,2,10,4,11,12,6,8,9] => [12,3,2,5,4,7,6,11,10,9,8,1] => [1,2,2,2,1,2,1,1]
[(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => [3,5,1,8,2,9,10,4,6,7,12,11] => [10,3,2,5,4,9,8,7,6,1,12,11] => [1,2,2,1,2,1,1,2]
[(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => [3,5,1,8,2,9,11,4,6,12,7,10] => [12,3,2,5,4,9,8,7,6,11,10,1] => [1,2,2,1,2,1,2,1]
[(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => [3,5,1,8,2,10,11,4,12,6,7,9] => [12,3,2,5,4,11,8,7,10,9,6,1] => [1,2,2,1,2,2,1,1]
[(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => [3,5,1,9,2,10,11,12,4,6,7,8] => [12,3,2,5,4,11,10,9,8,7,6,1] => [1,2,2,1,1,2,1,1,1]
[(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => [3,6,1,7,8,2,4,5,10,9,12,11] => [8,3,2,7,6,5,4,1,10,9,12,11] => [1,2,1,2,1,1,2,2]
[(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => [3,6,1,7,8,2,4,5,11,12,9,10] => [8,3,2,7,6,5,4,1,12,11,10,9] => [1,2,1,2,1,1,1,2,1]
[(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => [3,6,1,7,9,2,4,10,5,8,12,11] => [10,3,2,7,6,5,4,9,8,1,12,11] => [1,2,1,2,1,2,1,2]
[(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => [3,6,1,7,9,2,4,11,5,12,8,10] => [12,3,2,7,6,5,4,9,8,11,10,1] => [1,2,1,2,1,2,2,1]
[(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => [3,6,1,7,10,2,4,11,12,5,8,9] => [12,3,2,7,6,5,4,11,10,9,8,1] => [1,2,1,2,1,1,2,1,1]
[(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => [3,6,1,8,9,2,10,4,5,7,12,11] => [10,3,2,9,6,5,8,7,4,1,12,11] => [1,2,1,2,2,1,1,2]
[(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => [3,6,1,8,9,2,11,4,5,12,7,10] => [12,3,2,9,6,5,8,7,4,11,10,1] => [1,2,1,2,2,1,2,1]
[(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => [3,6,1,8,10,2,11,4,12,5,7,9] => [12,3,2,11,6,5,8,7,10,9,4,1] => [1,2,1,2,2,2,1,1]
[(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => [3,6,1,9,10,2,11,12,4,5,7,8] => [12,3,2,11,6,5,10,9,8,7,4,1] => [1,2,1,2,1,2,1,1,1]
[(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => [3,7,1,8,9,10,2,4,5,6,12,11] => [10,3,2,9,8,7,6,5,4,1,12,11] => [1,2,1,1,2,1,1,1,2]
[(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => [3,7,1,8,9,11,2,4,5,12,6,10] => [12,3,2,9,8,7,6,5,4,11,10,1] => [1,2,1,1,2,1,1,2,1]
[(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => [3,7,1,8,10,11,2,4,12,5,6,9] => [12,3,2,11,8,7,6,5,10,9,4,1] => [1,2,1,1,2,1,2,1,1]
[(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => [3,7,1,9,10,11,2,12,4,5,6,8] => [12,3,2,11,10,7,6,9,8,5,4,1] => [1,2,1,1,2,2,1,1,1]
[(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => [3,8,1,9,10,11,12,2,4,5,6,7] => [12,3,2,11,10,9,8,7,6,5,4,1] => [1,2,1,1,1,2,1,1,1,1]
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [6,5,4,3,2,1,8,7,10,9,12,11] => [1,1,2,1,1,2,2,2]
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [6,5,4,3,2,1,8,7,12,11,10,9] => [1,1,2,1,1,2,1,2,1]
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [6,5,4,3,2,1,10,9,8,7,12,11] => [1,1,2,1,1,1,2,1,2]
[(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => [4,5,6,1,2,3,9,11,7,12,8,10] => [6,5,4,3,2,1,12,9,8,11,10,7] => [1,1,2,1,1,1,2,2,1]
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [6,5,4,3,2,1,12,11,10,9,8,7] => [1,1,2,1,1,1,1,2,1,1]
[(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => [4,5,7,1,2,8,3,6,10,9,12,11] => [8,5,4,3,2,7,6,1,10,9,12,11] => [1,1,2,1,2,1,2,2]
[(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => [4,5,7,1,2,8,3,6,11,12,9,10] => [8,5,4,3,2,7,6,1,12,11,10,9] => [1,1,2,1,2,1,1,2,1]
[(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => [4,5,7,1,2,9,3,10,6,8,12,11] => [10,5,4,3,2,7,6,9,8,1,12,11] => [1,1,2,1,2,2,1,2]
[(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => [4,5,7,1,2,9,3,11,6,12,8,10] => [12,5,4,3,2,7,6,9,8,11,10,1] => [1,1,2,1,2,2,2,1]
[(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => [4,5,7,1,2,10,3,11,12,6,8,9] => [12,5,4,3,2,7,6,11,10,9,8,1] => [1,1,2,1,2,1,2,1,1]
[(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => [4,5,8,1,2,9,10,3,6,7,12,11] => [10,5,4,3,2,9,8,7,6,1,12,11] => [1,1,2,1,1,2,1,1,2]
[(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => [4,5,8,1,2,9,11,3,6,12,7,10] => [12,5,4,3,2,9,8,7,6,11,10,1] => [1,1,2,1,1,2,1,2,1]
[(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => [4,5,8,1,2,10,11,3,12,6,7,9] => [12,5,4,3,2,11,8,7,10,9,6,1] => [1,1,2,1,1,2,2,1,1]
[(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => [4,5,9,1,2,10,11,12,3,6,7,8] => [12,5,4,3,2,11,10,9,8,7,6,1] => [1,1,2,1,1,1,2,1,1,1]
[(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => [4,6,7,1,8,2,3,5,10,9,12,11] => [8,7,4,3,6,5,2,1,10,9,12,11] => [1,1,2,2,1,1,2,2]
[(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => [4,6,7,1,8,2,3,5,11,12,9,10] => [8,7,4,3,6,5,2,1,12,11,10,9] => [1,1,2,2,1,1,1,2,1]
[(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => [4,6,7,1,9,2,3,10,5,8,12,11] => [10,7,4,3,6,5,2,9,8,1,12,11] => [1,1,2,2,1,2,1,2]
[(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => [4,6,7,1,9,2,3,11,5,12,8,10] => [12,7,4,3,6,5,2,9,8,11,10,1] => [1,1,2,2,1,2,2,1]
[(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => [4,6,7,1,10,2,3,11,12,5,8,9] => [12,7,4,3,6,5,2,11,10,9,8,1] => [1,1,2,2,1,1,2,1,1]
[(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => [4,6,8,1,9,2,10,3,5,7,12,11] => [10,9,4,3,6,5,8,7,2,1,12,11] => [1,1,2,2,2,1,1,2]
[(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => [4,6,8,1,9,2,11,3,5,12,7,10] => [12,9,4,3,6,5,8,7,2,11,10,1] => [1,1,2,2,2,1,2,1]
[(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => [4,6,8,1,10,2,11,3,12,5,7,9] => [12,11,4,3,6,5,8,7,10,9,2,1] => [1,1,2,2,2,2,1,1]
[(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => [4,6,9,1,10,2,11,12,3,5,7,8] => [12,11,4,3,6,5,10,9,8,7,2,1] => [1,1,2,2,1,2,1,1,1]
[(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => [4,7,8,1,9,10,2,3,5,6,12,11] => [10,9,4,3,8,7,6,5,2,1,12,11] => [1,1,2,1,2,1,1,1,2]
[(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => [4,7,8,1,9,11,2,3,5,12,6,10] => [12,9,4,3,8,7,6,5,2,11,10,1] => [1,1,2,1,2,1,1,2,1]
[(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => [4,7,8,1,10,11,2,3,12,5,6,9] => [12,11,4,3,8,7,6,5,10,9,2,1] => [1,1,2,1,2,1,2,1,1]
[(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => [4,7,9,1,10,11,2,12,3,5,6,8] => [12,11,4,3,10,7,6,9,8,5,2,1] => [1,1,2,1,2,2,1,1,1]
[(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => [4,8,9,1,10,11,12,2,3,5,6,7] => [12,11,4,3,10,9,8,7,6,5,2,1] => [1,1,2,1,1,2,1,1,1,1]
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [8,7,6,5,4,3,2,1,10,9,12,11] => [1,1,1,2,1,1,1,2,2]
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [8,7,6,5,4,3,2,1,12,11,10,9] => [1,1,1,2,1,1,1,1,2,1]
[(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => [5,6,7,9,1,2,3,10,4,8,12,11] => [10,7,6,5,4,3,2,9,8,1,12,11] => [1,1,1,2,1,1,2,1,2]
[(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => [5,6,7,9,1,2,3,11,4,12,8,10] => [12,7,6,5,4,3,2,9,8,11,10,1] => [1,1,1,2,1,1,2,2,1]
[(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => [5,6,7,10,1,2,3,11,12,4,8,9] => [12,7,6,5,4,3,2,11,10,9,8,1] => [1,1,1,2,1,1,1,2,1,1]
[(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => [5,6,8,9,1,2,10,3,4,7,12,11] => [10,9,6,5,4,3,8,7,2,1,12,11] => [1,1,1,2,1,2,1,1,2]
[(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => [5,6,8,9,1,2,11,3,4,12,7,10] => [12,9,6,5,4,3,8,7,2,11,10,1] => [1,1,1,2,1,2,1,2,1]
[(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => [5,6,8,10,1,2,11,3,12,4,7,9] => [12,11,6,5,4,3,8,7,10,9,2,1] => [1,1,1,2,1,2,2,1,1]
[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => [5,6,9,10,1,2,11,12,3,4,7,8] => [12,11,6,5,4,3,10,9,8,7,2,1] => [1,1,1,2,1,1,2,1,1,1]
[(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => [5,7,8,9,1,10,2,3,4,6,12,11] => [10,9,8,5,4,7,6,3,2,1,12,11] => [1,1,1,2,2,1,1,1,2]
[(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => [5,7,8,9,1,11,2,3,4,12,6,10] => [12,9,8,5,4,7,6,3,2,11,10,1] => [1,1,1,2,2,1,1,2,1]
[(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => [5,7,8,10,1,11,2,3,12,4,6,9] => [12,11,8,5,4,7,6,3,10,9,2,1] => [1,1,1,2,2,1,2,1,1]
[(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => [5,7,9,10,1,11,2,12,3,4,6,8] => [12,11,10,5,4,7,6,9,8,3,2,1] => [1,1,1,2,2,2,1,1,1]
[(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => [5,8,9,10,1,11,12,2,3,4,6,7] => [12,11,10,5,4,9,8,7,6,3,2,1] => [1,1,1,2,1,2,1,1,1,1]
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [1,1,1,1,2,1,1,1,1,2]
[(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => [6,7,8,9,11,1,2,3,4,12,5,10] => [12,9,8,7,6,5,4,3,2,11,10,1] => [1,1,1,1,2,1,1,1,2,1]
[(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => [6,7,8,10,11,1,2,3,12,4,5,9] => [12,11,8,7,6,5,4,3,10,9,2,1] => [1,1,1,1,2,1,1,2,1,1]
[(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => [6,7,9,10,11,1,2,12,3,4,5,8] => [12,11,10,7,6,5,4,9,8,3,2,1] => [1,1,1,1,2,1,2,1,1,1]
[(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => [6,8,9,10,11,1,12,2,3,4,5,7] => [12,11,10,9,6,5,8,7,4,3,2,1] => [1,1,1,1,2,2,1,1,1,1]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,11,10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,2,1,1,1,1,1]
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
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
Map
DEX composition
Description
The DEX composition of a permutation.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.