Identifier
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
[(1,2)] => [2,1] => [2,1] => [1,1]
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [1,2,1]
[(1,3),(2,4)] => [3,4,1,2] => [3,1,4,2] => [1,2,1]
[(1,4),(2,3)] => [3,4,2,1] => [4,1,3,2] => [1,2,1]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,2,2,1]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [3,1,4,2,6,5] => [1,2,2,1]
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [4,1,3,2,6,5] => [1,2,2,1]
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [5,1,3,2,6,4] => [1,2,2,1]
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [6,1,3,2,5,4] => [1,2,2,1]
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [6,1,4,2,5,3] => [1,2,2,1]
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [5,1,4,2,6,3] => [1,2,2,1]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [1,2,2,1]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [3,1,5,2,6,4] => [1,2,2,1]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,5,3,6,4] => [1,2,2,1]
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [2,1,6,3,5,4] => [1,2,2,1]
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [3,1,6,2,5,4] => [1,2,2,1]
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [4,1,6,2,5,3] => [1,2,2,1]
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [6,2,5,1,4,3] => [1,2,2,1]
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => [1,2,2,1]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [1,2,2,2,1]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [3,1,4,2,6,5,8,7] => [1,2,2,2,1]
[(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [4,1,3,2,6,5,8,7] => [1,2,2,2,1]
[(1,5),(2,3),(4,6),(7,8)] => [3,5,2,6,1,4,8,7] => [5,1,3,2,6,4,8,7] => [1,2,2,2,1]
[(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [6,1,3,2,5,4,8,7] => [1,2,2,2,1]
[(1,7),(2,3),(4,5),(6,8)] => [3,5,2,7,4,8,1,6] => [7,1,3,2,5,4,8,6] => [1,2,2,2,1]
[(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [8,1,3,2,5,4,7,6] => [1,2,2,2,1]
[(1,8),(2,4),(3,5),(6,7)] => [4,5,7,2,3,8,6,1] => [8,1,4,2,5,3,7,6] => [1,2,2,2,1]
[(1,7),(2,4),(3,5),(6,8)] => [4,5,7,2,3,8,1,6] => [7,1,4,2,5,3,8,6] => [1,2,2,2,1]
[(1,6),(2,4),(3,5),(7,8)] => [4,5,6,2,3,1,8,7] => [6,1,4,2,5,3,8,7] => [1,2,2,2,1]
[(1,5),(2,4),(3,6),(7,8)] => [4,5,6,2,1,3,8,7] => [5,1,4,2,6,3,8,7] => [1,2,2,2,1]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [4,1,5,2,6,3,8,7] => [1,2,2,2,1]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [3,1,5,2,6,4,8,7] => [1,2,2,2,1]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,5,3,6,4,8,7] => [1,2,2,2,1]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [2,1,6,3,5,4,8,7] => [1,2,2,2,1]
[(1,3),(2,6),(4,5),(7,8)] => [3,5,1,6,4,2,8,7] => [3,1,6,2,5,4,8,7] => [1,2,2,2,1]
[(1,4),(2,6),(3,5),(7,8)] => [4,5,6,1,3,2,8,7] => [4,1,6,2,5,3,8,7] => [1,2,2,2,1]
[(1,5),(2,6),(3,4),(7,8)] => [4,5,6,3,1,2,8,7] => [6,2,5,1,4,3,8,7] => [1,2,2,2,1]
[(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [5,2,6,1,4,3,8,7] => [1,2,2,2,1]
[(1,7),(2,5),(3,4),(6,8)] => [4,5,7,3,2,8,1,6] => [5,2,7,1,4,3,8,6] => [1,2,2,2,1]
[(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [5,2,8,1,4,3,7,6] => [1,2,2,2,1]
[(1,8),(2,6),(3,4),(5,7)] => [4,6,7,3,8,2,5,1] => [6,2,8,1,4,3,7,5] => [1,2,2,2,1]
[(1,7),(2,6),(3,4),(5,8)] => [4,6,7,3,8,2,1,5] => [6,2,7,1,4,3,8,5] => [1,2,2,2,1]
[(1,6),(2,7),(3,4),(5,8)] => [4,6,7,3,8,1,2,5] => [7,2,6,1,4,3,8,5] => [1,2,2,2,1]
[(1,5),(2,7),(3,4),(6,8)] => [4,5,7,3,1,8,2,6] => [7,2,5,1,4,3,8,6] => [1,2,2,2,1]
[(1,4),(2,7),(3,5),(6,8)] => [4,5,7,1,3,8,2,6] => [4,1,7,2,5,3,8,6] => [1,2,2,2,1]
[(1,3),(2,7),(4,5),(6,8)] => [3,5,1,7,4,8,2,6] => [3,1,7,2,5,4,8,6] => [1,2,2,2,1]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,5,7,4,8,3,6] => [2,1,7,3,5,4,8,6] => [1,2,2,2,1]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [2,1,8,3,5,4,7,6] => [1,2,2,2,1]
[(1,3),(2,8),(4,5),(6,7)] => [3,5,1,7,4,8,6,2] => [3,1,8,2,5,4,7,6] => [1,2,2,2,1]
[(1,4),(2,8),(3,5),(6,7)] => [4,5,7,1,3,8,6,2] => [4,1,8,2,5,3,7,6] => [1,2,2,2,1]
[(1,5),(2,8),(3,4),(6,7)] => [4,5,7,3,1,8,6,2] => [8,2,5,1,4,3,7,6] => [1,2,2,2,1]
[(1,6),(2,8),(3,4),(5,7)] => [4,6,7,3,8,1,5,2] => [8,2,6,1,4,3,7,5] => [1,2,2,2,1]
[(1,7),(2,8),(3,4),(5,6)] => [4,6,7,3,8,5,1,2] => [7,1,4,3,8,2,6,5] => [1,2,2,2,1]
[(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [8,1,4,3,7,2,6,5] => [1,2,2,2,1]
[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => [8,1,5,3,7,2,6,4] => [1,2,2,2,1]
[(1,7),(2,8),(3,5),(4,6)] => [5,6,7,8,3,4,1,2] => [7,1,5,3,8,2,6,4] => [1,2,2,2,1]
[(1,6),(2,8),(3,5),(4,7)] => [5,6,7,8,3,1,4,2] => [8,2,6,1,5,3,7,4] => [1,2,2,2,1]
[(1,5),(2,8),(3,6),(4,7)] => [5,6,7,8,1,3,4,2] => [5,1,8,2,6,3,7,4] => [1,2,2,2,1]
[(1,4),(2,8),(3,6),(5,7)] => [4,6,7,1,8,3,5,2] => [4,1,8,2,6,3,7,5] => [1,2,2,2,1]
[(1,3),(2,8),(4,6),(5,7)] => [3,6,1,7,8,4,5,2] => [3,1,8,2,6,4,7,5] => [1,2,2,2,1]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,6,7,8,4,5,3] => [2,1,8,3,6,4,7,5] => [1,2,2,2,1]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,6,7,8,4,3,5] => [2,1,7,3,6,4,8,5] => [1,2,2,2,1]
[(1,3),(2,7),(4,6),(5,8)] => [3,6,1,7,8,4,2,5] => [3,1,7,2,6,4,8,5] => [1,2,2,2,1]
[(1,4),(2,7),(3,6),(5,8)] => [4,6,7,1,8,3,2,5] => [4,1,7,2,6,3,8,5] => [1,2,2,2,1]
[(1,5),(2,7),(3,6),(4,8)] => [5,6,7,8,1,3,2,4] => [5,1,7,2,6,3,8,4] => [1,2,2,2,1]
[(1,6),(2,7),(3,5),(4,8)] => [5,6,7,8,3,1,2,4] => [7,2,6,1,5,3,8,4] => [1,2,2,2,1]
[(1,7),(2,6),(3,5),(4,8)] => [5,6,7,8,3,2,1,4] => [6,2,7,1,5,3,8,4] => [1,2,2,2,1]
[(1,8),(2,6),(3,5),(4,7)] => [5,6,7,8,3,2,4,1] => [6,2,8,1,5,3,7,4] => [1,2,2,2,1]
[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => [8,1,5,2,6,3,7,4] => [1,2,2,2,1]
[(1,7),(2,5),(3,6),(4,8)] => [5,6,7,8,2,3,1,4] => [7,1,5,2,6,3,8,4] => [1,2,2,2,1]
[(1,6),(2,5),(3,7),(4,8)] => [5,6,7,8,2,1,3,4] => [6,1,5,2,7,3,8,4] => [1,2,2,2,1]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [5,1,6,2,7,3,8,4] => [1,2,2,2,1]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [4,1,6,2,7,3,8,5] => [1,2,2,2,1]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [3,1,6,2,7,4,8,5] => [1,2,2,2,1]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,6,3,7,4,8,5] => [1,2,2,2,1]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,5,3,7,4,8,6] => [1,2,2,2,1]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [3,1,5,2,7,4,8,6] => [1,2,2,2,1]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [4,1,5,2,7,3,8,6] => [1,2,2,2,1]
[(1,5),(2,4),(3,7),(6,8)] => [4,5,7,2,1,8,3,6] => [5,1,4,2,7,3,8,6] => [1,2,2,2,1]
[(1,6),(2,4),(3,7),(5,8)] => [4,6,7,2,8,1,3,5] => [6,1,4,2,7,3,8,5] => [1,2,2,2,1]
[(1,7),(2,4),(3,6),(5,8)] => [4,6,7,2,8,3,1,5] => [7,1,4,2,6,3,8,5] => [1,2,2,2,1]
[(1,8),(2,4),(3,6),(5,7)] => [4,6,7,2,8,3,5,1] => [8,1,4,2,6,3,7,5] => [1,2,2,2,1]
[(1,8),(2,3),(4,6),(5,7)] => [3,6,2,7,8,4,5,1] => [8,1,3,2,6,4,7,5] => [1,2,2,2,1]
[(1,7),(2,3),(4,6),(5,8)] => [3,6,2,7,8,4,1,5] => [7,1,3,2,6,4,8,5] => [1,2,2,2,1]
[(1,6),(2,3),(4,7),(5,8)] => [3,6,2,7,8,1,4,5] => [6,1,3,2,7,4,8,5] => [1,2,2,2,1]
[(1,5),(2,3),(4,7),(6,8)] => [3,5,2,7,1,8,4,6] => [5,1,3,2,7,4,8,6] => [1,2,2,2,1]
[(1,4),(2,3),(5,7),(6,8)] => [3,4,2,1,7,8,5,6] => [4,1,3,2,7,5,8,6] => [1,2,2,2,1]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [3,1,4,2,7,5,8,6] => [1,2,2,2,1]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,7,5,8,6] => [1,2,2,2,1]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [2,1,4,3,8,5,7,6] => [1,2,2,2,1]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,7,8,6,5] => [3,1,4,2,8,5,7,6] => [1,2,2,2,1]
[(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [4,1,3,2,8,5,7,6] => [1,2,2,2,1]
[(1,5),(2,3),(4,8),(6,7)] => [3,5,2,7,1,8,6,4] => [5,1,3,2,8,4,7,6] => [1,2,2,2,1]
[(1,6),(2,3),(4,8),(5,7)] => [3,6,2,7,8,1,5,4] => [6,1,3,2,8,4,7,5] => [1,2,2,2,1]
[(1,7),(2,3),(4,8),(5,6)] => [3,6,2,7,8,5,1,4] => [8,4,7,1,3,2,6,5] => [1,2,2,2,1]
[(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [7,4,8,1,3,2,6,5] => [1,2,2,2,1]
[(1,8),(2,4),(3,7),(5,6)] => [4,6,7,2,8,5,3,1] => [7,3,8,1,4,2,6,5] => [1,2,2,2,1]
[(1,7),(2,4),(3,8),(5,6)] => [4,6,7,2,8,5,1,3] => [8,3,7,1,4,2,6,5] => [1,2,2,2,1]
[(1,6),(2,4),(3,8),(5,7)] => [4,6,7,2,8,1,5,3] => [6,1,4,2,8,3,7,5] => [1,2,2,2,1]
[(1,5),(2,4),(3,8),(6,7)] => [4,5,7,2,1,8,6,3] => [5,1,4,2,8,3,7,6] => [1,2,2,2,1]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,7,1,2,8,6,3] => [4,1,5,2,8,3,7,6] => [1,2,2,2,1]
>>> Load all 323 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,7,2,8,6,4] => [3,1,5,2,8,4,7,6] => [1,2,2,2,1]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,7,3,8,6,4] => [2,1,5,3,8,4,7,6] => [1,2,2,2,1]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,7,8,3,5,4] => [2,1,6,3,8,4,7,5] => [1,2,2,2,1]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,7,8,2,5,4] => [3,1,6,2,8,4,7,5] => [1,2,2,2,1]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,7,1,8,2,5,3] => [4,1,6,2,8,3,7,5] => [1,2,2,2,1]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,7,8,1,2,4,3] => [5,1,6,2,8,3,7,4] => [1,2,2,2,1]
[(1,6),(2,5),(3,8),(4,7)] => [5,6,7,8,2,1,4,3] => [6,1,5,2,8,3,7,4] => [1,2,2,2,1]
[(1,7),(2,5),(3,8),(4,6)] => [5,6,7,8,2,4,1,3] => [8,3,7,1,5,2,6,4] => [1,2,2,2,1]
[(1,8),(2,5),(3,7),(4,6)] => [5,6,7,8,2,4,3,1] => [7,3,8,1,5,2,6,4] => [1,2,2,2,1]
[(1,8),(2,6),(3,7),(4,5)] => [5,6,7,8,4,2,3,1] => [6,2,7,3,8,1,5,4] => [1,2,2,2,1]
[(1,7),(2,6),(3,8),(4,5)] => [5,6,7,8,4,2,1,3] => [6,2,8,3,7,1,5,4] => [1,2,2,2,1]
[(1,6),(2,7),(3,8),(4,5)] => [5,6,7,8,4,1,2,3] => [8,3,7,2,6,1,5,4] => [1,2,2,2,1]
[(1,5),(2,7),(3,8),(4,6)] => [5,6,7,8,1,4,2,3] => [5,1,8,3,7,2,6,4] => [1,2,2,2,1]
[(1,4),(2,7),(3,8),(5,6)] => [4,6,7,1,8,5,2,3] => [4,1,8,3,7,2,6,5] => [1,2,2,2,1]
[(1,3),(2,7),(4,8),(5,6)] => [3,6,1,7,8,5,2,4] => [3,1,8,4,7,2,6,5] => [1,2,2,2,1]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,6,7,8,5,3,4] => [2,1,8,4,7,3,6,5] => [1,2,2,2,1]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [2,1,7,4,8,3,6,5] => [1,2,2,2,1]
[(1,3),(2,8),(4,7),(5,6)] => [3,6,1,7,8,5,4,2] => [3,1,7,4,8,2,6,5] => [1,2,2,2,1]
[(1,4),(2,8),(3,7),(5,6)] => [4,6,7,1,8,5,3,2] => [4,1,7,3,8,2,6,5] => [1,2,2,2,1]
[(1,5),(2,8),(3,7),(4,6)] => [5,6,7,8,1,4,3,2] => [5,1,7,3,8,2,6,4] => [1,2,2,2,1]
[(1,6),(2,8),(3,7),(4,5)] => [5,6,7,8,4,1,3,2] => [7,3,8,2,6,1,5,4] => [1,2,2,2,1]
[(1,7),(2,8),(3,6),(4,5)] => [5,6,7,8,4,3,1,2] => [8,2,6,3,7,1,5,4] => [1,2,2,2,1]
[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [7,2,6,3,8,1,5,4] => [1,2,2,2,1]
[(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] => [1,2,2,2,2,1]
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [3,1,4,2,6,5,8,7,10,9] => [1,2,2,2,2,1]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [3,4,2,1,6,5,8,7,10,9] => [4,1,3,2,6,5,8,7,10,9] => [1,2,2,2,2,1]
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [3,5,2,7,4,9,6,10,8,1] => [10,1,3,2,5,4,7,6,9,8] => [1,2,2,2,2,1]
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [4,1,5,2,6,3,8,7,10,9] => [1,2,2,2,2,1]
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [3,5,1,6,2,4,8,7,10,9] => [3,1,5,2,6,4,8,7,10,9] => [1,2,2,2,2,1]
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,5,3,6,4,8,7,10,9] => [1,2,2,2,2,1]
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,5,6,4,3,8,7,10,9] => [2,1,6,3,5,4,8,7,10,9] => [1,2,2,2,2,1]
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [5,1,6,2,7,3,8,4,10,9] => [1,2,2,2,2,1]
[(1,4),(2,6),(3,7),(5,8),(9,10)] => [4,6,7,1,8,2,3,5,10,9] => [4,1,6,2,7,3,8,5,10,9] => [1,2,2,2,2,1]
[(1,3),(2,6),(4,7),(5,8),(9,10)] => [3,6,1,7,8,2,4,5,10,9] => [3,1,6,2,7,4,8,5,10,9] => [1,2,2,2,2,1]
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,6,3,7,4,8,5,10,9] => [1,2,2,2,2,1]
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [2,1,5,7,3,8,4,6,10,9] => [2,1,5,3,7,4,8,6,10,9] => [1,2,2,2,2,1]
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [3,5,1,7,2,8,4,6,10,9] => [3,1,5,2,7,4,8,6,10,9] => [1,2,2,2,2,1]
[(1,4),(2,5),(3,7),(6,8),(9,10)] => [4,5,7,1,2,8,3,6,10,9] => [4,1,5,2,7,3,8,6,10,9] => [1,2,2,2,2,1]
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [3,1,4,2,7,5,8,6,10,9] => [1,2,2,2,2,1]
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,7,5,8,6,10,9] => [1,2,2,2,2,1]
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,7,8,6,5,10,9] => [2,1,4,3,8,5,7,6,10,9] => [1,2,2,2,2,1]
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [3,4,2,1,7,8,6,5,10,9] => [4,1,3,2,8,5,7,6,10,9] => [1,2,2,2,2,1]
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,7,3,8,4,9,5,10,6] => [1,2,2,2,2,1]
[(1,3),(2,7),(4,8),(5,9),(6,10)] => [3,7,1,8,9,10,2,4,5,6] => [3,1,7,2,8,4,9,5,10,6] => [1,2,2,2,2,1]
[(1,4),(2,7),(3,8),(5,9),(6,10)] => [4,7,8,1,9,10,2,3,5,6] => [4,1,7,2,8,3,9,5,10,6] => [1,2,2,2,2,1]
[(1,5),(2,7),(3,8),(4,9),(6,10)] => [5,7,8,9,1,10,2,3,4,6] => [5,1,7,2,8,3,9,4,10,6] => [1,2,2,2,2,1]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [6,1,7,2,8,3,9,4,10,5] => [1,2,2,2,2,1]
[(1,5),(2,6),(3,8),(4,9),(7,10)] => [5,6,8,9,1,2,10,3,4,7] => [5,1,6,2,8,3,9,4,10,7] => [1,2,2,2,2,1]
[(1,4),(2,6),(3,8),(5,9),(7,10)] => [4,6,8,1,9,2,10,3,5,7] => [4,1,6,2,8,3,9,5,10,7] => [1,2,2,2,2,1]
[(1,3),(2,6),(4,8),(5,9),(7,10)] => [3,6,1,8,9,2,10,4,5,7] => [3,1,6,2,8,4,9,5,10,7] => [1,2,2,2,2,1]
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [2,1,6,8,9,3,10,4,5,7] => [2,1,6,3,8,4,9,5,10,7] => [1,2,2,2,2,1]
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [2,1,5,8,3,9,10,4,6,7] => [2,1,5,3,8,4,9,6,10,7] => [1,2,2,2,2,1]
[(1,3),(2,5),(4,8),(6,9),(7,10)] => [3,5,1,8,2,9,10,4,6,7] => [3,1,5,2,8,4,9,6,10,7] => [1,2,2,2,2,1]
[(1,4),(2,5),(3,8),(6,9),(7,10)] => [4,5,8,1,2,9,10,3,6,7] => [4,1,5,2,8,3,9,6,10,7] => [1,2,2,2,2,1]
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [3,1,4,2,8,5,9,6,10,7] => [1,2,2,2,2,1]
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,8,5,9,6,10,7] => [1,2,2,2,2,1]
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [2,1,4,3,7,9,5,10,6,8] => [2,1,4,3,7,5,9,6,10,8] => [1,2,2,2,2,1]
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [3,4,1,2,7,9,5,10,6,8] => [3,1,4,2,7,5,9,6,10,8] => [1,2,2,2,2,1]
[(1,4),(2,5),(3,7),(6,9),(8,10)] => [4,5,7,1,2,9,3,10,6,8] => [4,1,5,2,7,3,9,6,10,8] => [1,2,2,2,2,1]
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8] => [3,1,5,2,7,4,9,6,10,8] => [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] => [2,1,5,3,7,4,9,6,10,8] => [1,2,2,2,2,1]
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [2,1,6,7,9,3,4,10,5,8] => [2,1,6,3,7,4,9,5,10,8] => [1,2,2,2,2,1]
[(1,3),(2,6),(4,7),(5,9),(8,10)] => [3,6,1,7,9,2,4,10,5,8] => [3,1,6,2,7,4,9,5,10,8] => [1,2,2,2,2,1]
[(1,4),(2,6),(3,7),(5,9),(8,10)] => [4,6,7,1,9,2,3,10,5,8] => [4,1,6,2,7,3,9,5,10,8] => [1,2,2,2,2,1]
[(1,5),(2,6),(3,7),(4,9),(8,10)] => [5,6,7,9,1,2,3,10,4,8] => [5,1,6,2,7,3,9,4,10,8] => [1,2,2,2,2,1]
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,5,3,6,4,9,7,10,8] => [1,2,2,2,2,1]
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [3,5,1,6,2,4,9,10,7,8] => [3,1,5,2,6,4,9,7,10,8] => [1,2,2,2,2,1]
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [4,1,5,2,6,3,9,7,10,8] => [1,2,2,2,2,1]
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [3,1,4,2,6,5,9,7,10,8] => [1,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,9,7,10,8] => [1,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,9,10,8,7] => [2,1,4,3,6,5,10,7,9,8] => [1,2,2,2,2,1]
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [3,4,2,1,6,5,9,10,8,7] => [4,1,3,2,6,5,10,7,9,8] => [1,2,2,2,2,1]
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,5,6,4,3,9,10,8,7] => [2,1,6,3,5,4,10,7,9,8] => [1,2,2,2,2,1]
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,7,8,6,5,10,9,12,11] => [2,1,4,3,8,5,7,6,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [3,4,2,1,7,8,6,5,10,9,12,11] => [4,1,3,2,8,5,7,6,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,7,8,6,5,11,12,10,9] => [2,1,4,3,8,5,7,6,12,9,11,10] => [1,2,2,2,2,2,1]
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [3,4,2,1,7,8,6,5,11,12,10,9] => [4,1,3,2,8,5,7,6,12,9,11,10] => [1,2,2,2,2,2,1]
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [3,5,2,7,4,9,6,11,8,12,10,1] => [12,1,3,2,5,4,7,6,9,8,11,10] => [1,2,2,2,2,2,1]
[(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] => [1,2,2,2,2,2,1]
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [3,4,2,1,6,5,8,7,10,9,12,11] => [4,1,3,2,6,5,8,7,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,11,12,10,9] => [2,1,4,3,6,5,8,7,12,9,11,10] => [1,2,2,2,2,2,1]
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [3,4,2,1,6,5,8,7,11,12,10,9] => [4,1,3,2,6,5,8,7,12,9,11,10] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,5,6,4,3,8,7,10,9,12,11] => [2,1,6,3,5,4,8,7,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,5,6,4,3,8,7,11,12,10,9] => [2,1,6,3,5,4,8,7,12,9,11,10] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,9,10,8,7,12,11] => [2,1,4,3,6,5,10,7,9,8,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [3,4,2,1,6,5,9,10,8,7,12,11] => [4,1,3,2,6,5,10,7,9,8,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,5,6,4,3,9,10,8,7,12,11] => [2,1,6,3,5,4,10,7,9,8,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13] => [1,2,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15] => [1,2,2,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,9,7,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => [2,1,4,3,6,5,9,11,7,12,8,10] => [2,1,4,3,6,5,9,7,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,10,7,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,7,5,8,6,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,7,5,8,6,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => [2,1,4,3,7,9,5,10,6,8,12,11] => [2,1,4,3,7,5,9,6,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => [2,1,4,3,7,9,5,11,6,12,8,10] => [2,1,4,3,7,5,9,6,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => [2,1,4,3,7,10,5,11,12,6,8,9] => [2,1,4,3,7,5,10,6,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,8,5,9,6,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => [2,1,4,3,8,9,11,5,6,12,7,10] => [2,1,4,3,8,5,9,6,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => [2,1,4,3,8,10,11,5,12,6,7,9] => [2,1,4,3,8,5,10,6,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,9,5,10,6,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,5,3,6,4,8,7,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,5,3,6,4,8,7,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,5,3,6,4,9,7,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => [2,1,5,6,3,4,9,11,7,12,8,10] => [2,1,5,3,6,4,9,7,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,5,3,6,4,10,7,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => [2,1,5,7,3,8,4,6,10,9,12,11] => [2,1,5,3,7,4,8,6,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => [2,1,5,7,3,8,4,6,11,12,9,10] => [2,1,5,3,7,4,8,6,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => [2,1,5,7,3,9,4,10,6,8,12,11] => [2,1,5,3,7,4,9,6,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => [2,1,5,7,3,9,4,11,6,12,8,10] => [2,1,5,3,7,4,9,6,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => [2,1,5,7,3,10,4,11,12,6,8,9] => [2,1,5,3,7,4,10,6,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => [2,1,5,8,3,9,10,4,6,7,12,11] => [2,1,5,3,8,4,9,6,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => [2,1,5,8,3,9,11,4,6,12,7,10] => [2,1,5,3,8,4,9,6,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => [2,1,5,8,3,10,11,4,12,6,7,9] => [2,1,5,3,8,4,10,6,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => [2,1,5,9,3,10,11,12,4,6,7,8] => [2,1,5,3,9,4,10,6,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,6,3,7,4,8,5,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,6,3,7,4,8,5,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => [2,1,6,7,9,3,4,10,5,8,12,11] => [2,1,6,3,7,4,9,5,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => [2,1,6,7,9,3,4,11,5,12,8,10] => [2,1,6,3,7,4,9,5,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => [2,1,6,7,10,3,4,11,12,5,8,9] => [2,1,6,3,7,4,10,5,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => [2,1,6,8,9,3,10,4,5,7,12,11] => [2,1,6,3,8,4,9,5,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => [2,1,6,8,9,3,11,4,5,12,7,10] => [2,1,6,3,8,4,9,5,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => [2,1,6,8,10,3,11,4,12,5,7,9] => [2,1,6,3,8,4,10,5,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => [2,1,6,9,10,3,11,12,4,5,7,8] => [2,1,6,3,9,4,10,5,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,7,3,8,4,9,5,10,6,12,11] => [1,2,2,2,2,2,1]
[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => [2,1,7,8,9,11,3,4,5,12,6,10] => [2,1,7,3,8,4,9,5,11,6,12,10] => [1,2,2,2,2,2,1]
[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => [2,1,7,8,10,11,3,4,12,5,6,9] => [2,1,7,3,8,4,10,5,11,6,12,9] => [1,2,2,2,2,2,1]
[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => [2,1,7,9,10,11,3,12,4,5,6,8] => [2,1,7,3,9,4,10,5,11,6,12,8] => [1,2,2,2,2,2,1]
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,8,3,9,4,10,5,11,6,12,7] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [3,1,4,2,6,5,8,7,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [3,1,4,2,6,5,8,7,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [3,1,4,2,6,5,9,7,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => [3,4,1,2,6,5,9,11,7,12,8,10] => [3,1,4,2,6,5,9,7,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [3,1,4,2,6,5,10,7,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [3,1,4,2,7,5,8,6,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [3,1,4,2,7,5,8,6,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => [3,4,1,2,7,9,5,10,6,8,12,11] => [3,1,4,2,7,5,9,6,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => [3,4,1,2,7,9,5,11,6,12,8,10] => [3,1,4,2,7,5,9,6,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => [3,4,1,2,7,10,5,11,12,6,8,9] => [3,1,4,2,7,5,10,6,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [3,1,4,2,8,5,9,6,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => [3,4,1,2,8,9,11,5,6,12,7,10] => [3,1,4,2,8,5,9,6,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => [3,4,1,2,8,10,11,5,12,6,7,9] => [3,1,4,2,8,5,10,6,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [3,1,4,2,9,5,10,6,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => [3,5,1,6,2,4,8,7,10,9,12,11] => [3,1,5,2,6,4,8,7,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => [3,5,1,6,2,4,8,7,11,12,9,10] => [3,1,5,2,6,4,8,7,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => [3,5,1,6,2,4,9,10,7,8,12,11] => [3,1,5,2,6,4,9,7,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => [3,5,1,6,2,4,9,11,7,12,8,10] => [3,1,5,2,6,4,9,7,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => [3,5,1,6,2,4,10,11,12,7,8,9] => [3,1,5,2,6,4,10,7,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => [3,5,1,7,2,8,4,6,10,9,12,11] => [3,1,5,2,7,4,8,6,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => [3,5,1,7,2,8,4,6,11,12,9,10] => [3,1,5,2,7,4,8,6,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => [3,5,1,7,2,9,4,10,6,8,12,11] => [3,1,5,2,7,4,9,6,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => [3,5,1,7,2,9,4,11,6,12,8,10] => [3,1,5,2,7,4,9,6,11,8,12,10] => [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] => [3,1,5,2,7,4,10,6,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => [3,5,1,8,2,9,10,4,6,7,12,11] => [3,1,5,2,8,4,9,6,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => [3,5,1,8,2,9,11,4,6,12,7,10] => [3,1,5,2,8,4,9,6,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => [3,5,1,8,2,10,11,4,12,6,7,9] => [3,1,5,2,8,4,10,6,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => [3,5,1,9,2,10,11,12,4,6,7,8] => [3,1,5,2,9,4,10,6,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => [3,6,1,7,8,2,4,5,10,9,12,11] => [3,1,6,2,7,4,8,5,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => [3,6,1,7,8,2,4,5,11,12,9,10] => [3,1,6,2,7,4,8,5,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => [3,6,1,7,9,2,4,10,5,8,12,11] => [3,1,6,2,7,4,9,5,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => [3,6,1,7,9,2,4,11,5,12,8,10] => [3,1,6,2,7,4,9,5,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => [3,6,1,7,10,2,4,11,12,5,8,9] => [3,1,6,2,7,4,10,5,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => [3,6,1,8,9,2,10,4,5,7,12,11] => [3,1,6,2,8,4,9,5,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => [3,6,1,8,9,2,11,4,5,12,7,10] => [3,1,6,2,8,4,9,5,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => [3,6,1,8,10,2,11,4,12,5,7,9] => [3,1,6,2,8,4,10,5,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => [3,6,1,9,10,2,11,12,4,5,7,8] => [3,1,6,2,9,4,10,5,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => [3,7,1,8,9,10,2,4,5,6,12,11] => [3,1,7,2,8,4,9,5,10,6,12,11] => [1,2,2,2,2,2,1]
[(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => [3,7,1,8,9,11,2,4,5,12,6,10] => [3,1,7,2,8,4,9,5,11,6,12,10] => [1,2,2,2,2,2,1]
[(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => [3,7,1,8,10,11,2,4,12,5,6,9] => [3,1,7,2,8,4,10,5,11,6,12,9] => [1,2,2,2,2,2,1]
[(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => [3,7,1,9,10,11,2,12,4,5,6,8] => [3,1,7,2,9,4,10,5,11,6,12,8] => [1,2,2,2,2,2,1]
[(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => [3,8,1,9,10,11,12,2,4,5,6,7] => [3,1,8,2,9,4,10,5,11,6,12,7] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [4,1,5,2,6,3,8,7,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [4,1,5,2,6,3,8,7,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [4,1,5,2,6,3,9,7,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => [4,5,6,1,2,3,9,11,7,12,8,10] => [4,1,5,2,6,3,9,7,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [4,1,5,2,6,3,10,7,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => [4,5,7,1,2,8,3,6,10,9,12,11] => [4,1,5,2,7,3,8,6,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => [4,5,7,1,2,8,3,6,11,12,9,10] => [4,1,5,2,7,3,8,6,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => [4,5,7,1,2,9,3,10,6,8,12,11] => [4,1,5,2,7,3,9,6,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => [4,5,7,1,2,9,3,11,6,12,8,10] => [4,1,5,2,7,3,9,6,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => [4,5,7,1,2,10,3,11,12,6,8,9] => [4,1,5,2,7,3,10,6,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => [4,5,8,1,2,9,10,3,6,7,12,11] => [4,1,5,2,8,3,9,6,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => [4,5,8,1,2,9,11,3,6,12,7,10] => [4,1,5,2,8,3,9,6,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => [4,5,8,1,2,10,11,3,12,6,7,9] => [4,1,5,2,8,3,10,6,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => [4,5,9,1,2,10,11,12,3,6,7,8] => [4,1,5,2,9,3,10,6,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => [4,6,7,1,8,2,3,5,10,9,12,11] => [4,1,6,2,7,3,8,5,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => [4,6,7,1,8,2,3,5,11,12,9,10] => [4,1,6,2,7,3,8,5,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => [4,6,7,1,9,2,3,10,5,8,12,11] => [4,1,6,2,7,3,9,5,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => [4,6,7,1,9,2,3,11,5,12,8,10] => [4,1,6,2,7,3,9,5,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => [4,6,7,1,10,2,3,11,12,5,8,9] => [4,1,6,2,7,3,10,5,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => [4,6,8,1,9,2,10,3,5,7,12,11] => [4,1,6,2,8,3,9,5,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => [4,6,8,1,9,2,11,3,5,12,7,10] => [4,1,6,2,8,3,9,5,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => [4,6,8,1,10,2,11,3,12,5,7,9] => [4,1,6,2,8,3,10,5,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => [4,6,9,1,10,2,11,12,3,5,7,8] => [4,1,6,2,9,3,10,5,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => [4,7,8,1,9,10,2,3,5,6,12,11] => [4,1,7,2,8,3,9,5,10,6,12,11] => [1,2,2,2,2,2,1]
[(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => [4,7,8,1,9,11,2,3,5,12,6,10] => [4,1,7,2,8,3,9,5,11,6,12,10] => [1,2,2,2,2,2,1]
[(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => [4,7,8,1,10,11,2,3,12,5,6,9] => [4,1,7,2,8,3,10,5,11,6,12,9] => [1,2,2,2,2,2,1]
[(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => [4,7,9,1,10,11,2,12,3,5,6,8] => [4,1,7,2,9,3,10,5,11,6,12,8] => [1,2,2,2,2,2,1]
[(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => [4,8,9,1,10,11,12,2,3,5,6,7] => [4,1,8,2,9,3,10,5,11,6,12,7] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [5,1,6,2,7,3,8,4,10,9,12,11] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [5,1,6,2,7,3,8,4,11,9,12,10] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => [5,6,7,9,1,2,3,10,4,8,12,11] => [5,1,6,2,7,3,9,4,10,8,12,11] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => [5,6,7,9,1,2,3,11,4,12,8,10] => [5,1,6,2,7,3,9,4,11,8,12,10] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => [5,6,7,10,1,2,3,11,12,4,8,9] => [5,1,6,2,7,3,10,4,11,8,12,9] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => [5,6,8,9,1,2,10,3,4,7,12,11] => [5,1,6,2,8,3,9,4,10,7,12,11] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => [5,6,8,9,1,2,11,3,4,12,7,10] => [5,1,6,2,8,3,9,4,11,7,12,10] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => [5,6,8,10,1,2,11,3,12,4,7,9] => [5,1,6,2,8,3,10,4,11,7,12,9] => [1,2,2,2,2,2,1]
[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => [5,6,9,10,1,2,11,12,3,4,7,8] => [5,1,6,2,9,3,10,4,11,7,12,8] => [1,2,2,2,2,2,1]
[(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => [5,7,8,9,1,10,2,3,4,6,12,11] => [5,1,7,2,8,3,9,4,10,6,12,11] => [1,2,2,2,2,2,1]
[(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => [5,7,8,9,1,11,2,3,4,12,6,10] => [5,1,7,2,8,3,9,4,11,6,12,10] => [1,2,2,2,2,2,1]
[(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => [5,7,8,10,1,11,2,3,12,4,6,9] => [5,1,7,2,8,3,10,4,11,6,12,9] => [1,2,2,2,2,2,1]
[(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => [5,7,9,10,1,11,2,12,3,4,6,8] => [5,1,7,2,9,3,10,4,11,6,12,8] => [1,2,2,2,2,2,1]
[(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => [5,8,9,10,1,11,12,2,3,4,6,7] => [5,1,8,2,9,3,10,4,11,6,12,7] => [1,2,2,2,2,2,1]
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [6,1,7,2,8,3,9,4,10,5,12,11] => [1,2,2,2,2,2,1]
[(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => [6,7,8,9,11,1,2,3,4,12,5,10] => [6,1,7,2,8,3,9,4,11,5,12,10] => [1,2,2,2,2,2,1]
[(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => [6,7,8,10,11,1,2,3,12,4,5,9] => [6,1,7,2,8,3,10,4,11,5,12,9] => [1,2,2,2,2,2,1]
[(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => [6,7,9,10,11,1,2,12,3,4,5,8] => [6,1,7,2,9,3,10,4,11,5,12,8] => [1,2,2,2,2,2,1]
[(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => [6,8,9,10,11,1,12,2,3,4,5,7] => [6,1,8,2,9,3,10,4,11,5,12,7] => [1,2,2,2,2,2,1]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [7,1,8,2,9,3,10,4,11,5,12,6] => [1,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] => [1,2,2,2,2,2,2,2,2,1]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17,20,19] => [2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17,20,19] => [1,2,2,2,2,2,2,2,2,2,1]
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
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.