Processing math: 100%

Identifier
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
[(1,2)] => [2,1] => [1,2] => [2]
[(1,2),(3,4)] => [2,1,4,3] => [3,4,1,2] => [2,2]
[(1,3),(2,4)] => [3,4,1,2] => [2,1,4,3] => [1,2,1]
[(1,4),(2,3)] => [3,4,2,1] => [2,1,3,4] => [1,3]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [2,2,2]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,3,6,5,1,2] => [1,2,1,2]
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [4,3,5,6,1,2] => [1,3,2]
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [4,2,5,1,6,3] => [1,2,2,1]
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [4,2,5,1,3,6] => [1,2,3]
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [3,2,1,5,4,6] => [1,1,2,2]
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [3,2,1,5,6,4] => [1,1,3,1]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,2,1,1]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => [1,2,2,1]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [5,6,2,1,4,3] => [2,1,2,1]
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [5,6,2,1,3,4] => [2,1,3]
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [4,2,6,1,3,5] => [1,2,3]
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [3,2,1,6,4,5] => [1,1,2,2]
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [3,2,1,4,6,5] => [1,1,3,1]
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [3,2,1,4,5,6] => [1,1,4]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [6,5,8,7,3,4,1,2] => [1,2,1,2,2]
[(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [6,5,7,8,3,4,1,2] => [1,3,2,2]
[(1,5),(2,3),(4,6),(7,8)] => [3,5,2,6,1,4,8,7] => [6,4,7,3,8,5,1,2] => [1,2,2,1,2]
[(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [6,4,7,3,5,8,1,2] => [1,2,3,2]
[(1,7),(2,3),(4,5),(6,8)] => [3,5,2,7,4,8,1,6] => [6,4,7,2,5,1,8,3] => [1,2,2,2,1]
[(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
[(1,8),(2,4),(3,5),(6,7)] => [4,5,7,2,3,8,6,1] => [5,4,2,7,6,1,3,8] => [1,1,2,1,3]
[(1,7),(2,4),(3,5),(6,8)] => [4,5,7,2,3,8,1,6] => [5,4,2,7,6,1,8,3] => [1,1,2,1,2,1]
[(1,6),(2,4),(3,5),(7,8)] => [4,5,6,2,3,1,8,7] => [5,4,3,7,6,8,1,2] => [1,1,2,2,2]
[(1,5),(2,4),(3,6),(7,8)] => [4,5,6,2,1,3,8,7] => [5,4,3,7,8,6,1,2] => [1,1,3,1,2]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [5,4,3,8,7,6,1,2] => [1,1,2,1,1,2]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [6,4,8,3,7,5,1,2] => [1,2,2,1,2]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => [2,1,2,1,2]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [7,8,4,3,5,6,1,2] => [2,1,3,2]
[(1,3),(2,6),(4,5),(7,8)] => [3,5,1,6,4,2,8,7] => [6,4,8,3,5,7,1,2] => [1,2,3,2]
[(1,4),(2,6),(3,5),(7,8)] => [4,5,6,1,3,2,8,7] => [5,4,3,8,6,7,1,2] => [1,1,2,2,2]
[(1,5),(2,6),(3,4),(7,8)] => [4,5,6,3,1,2,8,7] => [5,4,3,6,8,7,1,2] => [1,1,3,1,2]
[(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [5,4,3,6,7,8,1,2] => [1,1,4,2]
[(1,7),(2,5),(3,4),(6,8)] => [4,5,7,3,2,8,1,6] => [5,4,2,6,7,1,8,3] => [1,1,3,2,1]
[(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [5,4,2,6,7,1,3,8] => [1,1,3,3]
[(1,8),(2,6),(3,4),(5,7)] => [4,6,7,3,8,2,5,1] => [5,3,2,6,1,7,4,8] => [1,1,2,2,2]
[(1,7),(2,6),(3,4),(5,8)] => [4,6,7,3,8,2,1,5] => [5,3,2,6,1,7,8,4] => [1,1,2,3,1]
[(1,6),(2,7),(3,4),(5,8)] => [4,6,7,3,8,1,2,5] => [5,3,2,6,1,8,7,4] => [1,1,2,2,1,1]
[(1,5),(2,7),(3,4),(6,8)] => [4,5,7,3,1,8,2,6] => [5,4,2,6,8,1,7,3] => [1,1,3,2,1]
[(1,4),(2,7),(3,5),(6,8)] => [4,5,7,1,3,8,2,6] => [5,4,2,8,6,1,7,3] => [1,1,2,1,2,1]
[(1,3),(2,7),(4,5),(6,8)] => [3,5,1,7,4,8,2,6] => [6,4,8,2,5,1,7,3] => [1,2,2,2,1]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,5,7,4,8,3,6] => [7,8,4,2,5,1,6,3] => [2,1,2,2,1]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [7,8,4,2,5,1,3,6] => [2,1,2,3]
[(1,3),(2,8),(4,5),(6,7)] => [3,5,1,7,4,8,6,2] => [6,4,8,2,5,1,3,7] => [1,2,2,3]
[(1,4),(2,8),(3,5),(6,7)] => [4,5,7,1,3,8,6,2] => [5,4,2,8,6,1,3,7] => [1,1,2,1,3]
[(1,5),(2,8),(3,4),(6,7)] => [4,5,7,3,1,8,6,2] => [5,4,2,6,8,1,3,7] => [1,1,3,3]
[(1,6),(2,8),(3,4),(5,7)] => [4,6,7,3,8,1,5,2] => [5,3,2,6,1,8,4,7] => [1,1,2,2,2]
[(1,7),(2,8),(3,4),(5,6)] => [4,6,7,3,8,5,1,2] => [5,3,2,6,1,4,8,7] => [1,1,2,3,1]
[(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [5,3,2,6,1,4,7,8] => [1,1,2,4]
[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => [4,3,2,1,6,5,7,8] => [1,1,1,2,3]
[(1,7),(2,8),(3,5),(4,6)] => [5,6,7,8,3,4,1,2] => [4,3,2,1,6,5,8,7] => [1,1,1,2,2,1]
[(1,6),(2,8),(3,5),(4,7)] => [5,6,7,8,3,1,4,2] => [4,3,2,1,6,8,5,7] => [1,1,1,3,2]
[(1,5),(2,8),(3,6),(4,7)] => [5,6,7,8,1,3,4,2] => [4,3,2,1,8,6,5,7] => [1,1,1,2,1,2]
[(1,4),(2,8),(3,6),(5,7)] => [4,6,7,1,8,3,5,2] => [5,3,2,8,1,6,4,7] => [1,1,2,2,2]
[(1,3),(2,8),(4,6),(5,7)] => [3,6,1,7,8,4,5,2] => [6,3,8,2,1,5,4,7] => [1,2,1,2,2]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,6,7,8,4,5,3] => [7,8,3,2,1,5,4,6] => [2,1,1,2,2]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,6,7,8,4,3,5] => [7,8,3,2,1,5,6,4] => [2,1,1,3,1]
[(1,3),(2,7),(4,6),(5,8)] => [3,6,1,7,8,4,2,5] => [6,3,8,2,1,5,7,4] => [1,2,1,3,1]
[(1,4),(2,7),(3,6),(5,8)] => [4,6,7,1,8,3,2,5] => [5,3,2,8,1,6,7,4] => [1,1,2,3,1]
[(1,5),(2,7),(3,6),(4,8)] => [5,6,7,8,1,3,2,4] => [4,3,2,1,8,6,7,5] => [1,1,1,2,2,1]
[(1,6),(2,7),(3,5),(4,8)] => [5,6,7,8,3,1,2,4] => [4,3,2,1,6,8,7,5] => [1,1,1,3,1,1]
[(1,7),(2,6),(3,5),(4,8)] => [5,6,7,8,3,2,1,4] => [4,3,2,1,6,7,8,5] => [1,1,1,4,1]
[(1,8),(2,6),(3,5),(4,7)] => [5,6,7,8,3,2,4,1] => [4,3,2,1,6,7,5,8] => [1,1,1,3,2]
[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => [4,3,2,1,7,6,5,8] => [1,1,1,2,1,2]
[(1,7),(2,5),(3,6),(4,8)] => [5,6,7,8,2,3,1,4] => [4,3,2,1,7,6,8,5] => [1,1,1,2,2,1]
[(1,6),(2,5),(3,7),(4,8)] => [5,6,7,8,2,1,3,4] => [4,3,2,1,7,8,6,5] => [1,1,1,3,1,1]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [1,1,1,2,1,1,1]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [5,3,2,8,1,7,6,4] => [1,1,2,2,1,1]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [6,3,8,2,1,7,5,4] => [1,2,1,2,1,1]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [7,8,3,2,1,6,5,4] => [2,1,1,2,1,1]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [7,8,4,2,6,1,5,3] => [2,1,2,2,1]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [6,4,8,2,7,1,5,3] => [1,2,2,2,1]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [5,4,2,8,7,1,6,3] => [1,1,2,1,2,1]
[(1,5),(2,4),(3,7),(6,8)] => [4,5,7,2,1,8,3,6] => [5,4,2,7,8,1,6,3] => [1,1,3,2,1]
[(1,6),(2,4),(3,7),(5,8)] => [4,6,7,2,8,1,3,5] => [5,3,2,7,1,8,6,4] => [1,1,2,2,1,1]
[(1,7),(2,4),(3,6),(5,8)] => [4,6,7,2,8,3,1,5] => [5,3,2,7,1,6,8,4] => [1,1,2,3,1]
[(1,8),(2,4),(3,6),(5,7)] => [4,6,7,2,8,3,5,1] => [5,3,2,7,1,6,4,8] => [1,1,2,2,2]
[(1,8),(2,3),(4,6),(5,7)] => [3,6,2,7,8,4,5,1] => [6,3,7,2,1,5,4,8] => [1,2,1,2,2]
[(1,7),(2,3),(4,6),(5,8)] => [3,6,2,7,8,4,1,5] => [6,3,7,2,1,5,8,4] => [1,2,1,3,1]
[(1,6),(2,3),(4,7),(5,8)] => [3,6,2,7,8,1,4,5] => [6,3,7,2,1,8,5,4] => [1,2,1,2,1,1]
[(1,5),(2,3),(4,7),(6,8)] => [3,5,2,7,1,8,4,6] => [6,4,7,2,8,1,5,3] => [1,2,2,2,1]
[(1,4),(2,3),(5,7),(6,8)] => [3,4,2,1,7,8,5,6] => [6,5,7,8,2,1,4,3] => [1,3,1,2,1]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => [1,2,1,1,2,1]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [7,8,5,6,2,1,4,3] => [2,2,1,2,1]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [7,8,5,6,2,1,3,4] => [2,2,1,3]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,7,8,6,5] => [6,5,8,7,2,1,3,4] => [1,2,1,1,3]
[(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [6,5,7,8,2,1,3,4] => [1,3,1,3]
[(1,5),(2,3),(4,8),(6,7)] => [3,5,2,7,1,8,6,4] => [6,4,7,2,8,1,3,5] => [1,2,2,3]
[(1,6),(2,3),(4,8),(5,7)] => [3,6,2,7,8,1,5,4] => [6,3,7,2,1,8,4,5] => [1,2,1,2,2]
[(1,7),(2,3),(4,8),(5,6)] => [3,6,2,7,8,5,1,4] => [6,3,7,2,1,4,8,5] => [1,2,1,3,1]
[(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [6,3,7,2,1,4,5,8] => [1,2,1,4]
[(1,8),(2,4),(3,7),(5,6)] => [4,6,7,2,8,5,3,1] => [5,3,2,7,1,4,6,8] => [1,1,2,4]
[(1,7),(2,4),(3,8),(5,6)] => [4,6,7,2,8,5,1,3] => [5,3,2,7,1,4,8,6] => [1,1,2,3,1]
[(1,6),(2,4),(3,8),(5,7)] => [4,6,7,2,8,1,5,3] => [5,3,2,7,1,8,4,6] => [1,1,2,2,2]
[(1,5),(2,4),(3,8),(6,7)] => [4,5,7,2,1,8,6,3] => [5,4,2,7,8,1,3,6] => [1,1,3,3]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,7,1,2,8,6,3] => [5,4,2,8,7,1,3,6] => [1,1,2,1,3]
>>> Load all 307 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,7,2,8,6,4] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,7,3,8,6,4] => [7,8,4,2,6,1,3,5] => [2,1,2,3]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,7,8,3,5,4] => [7,8,3,2,1,6,4,5] => [2,1,1,2,2]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,7,8,2,5,4] => [6,3,8,2,1,7,4,5] => [1,2,1,2,2]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,7,1,8,2,5,3] => [5,3,2,8,1,7,4,6] => [1,1,2,2,2]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,7,8,1,2,4,3] => [4,3,2,1,8,7,5,6] => [1,1,1,2,1,2]
[(1,6),(2,5),(3,8),(4,7)] => [5,6,7,8,2,1,4,3] => [4,3,2,1,7,8,5,6] => [1,1,1,3,2]
[(1,7),(2,5),(3,8),(4,6)] => [5,6,7,8,2,4,1,3] => [4,3,2,1,7,5,8,6] => [1,1,1,2,2,1]
[(1,8),(2,5),(3,7),(4,6)] => [5,6,7,8,2,4,3,1] => [4,3,2,1,7,5,6,8] => [1,1,1,2,3]
[(1,8),(2,6),(3,7),(4,5)] => [5,6,7,8,4,2,3,1] => [4,3,2,1,5,7,6,8] => [1,1,1,3,2]
[(1,7),(2,6),(3,8),(4,5)] => [5,6,7,8,4,2,1,3] => [4,3,2,1,5,7,8,6] => [1,1,1,4,1]
[(1,6),(2,7),(3,8),(4,5)] => [5,6,7,8,4,1,2,3] => [4,3,2,1,5,8,7,6] => [1,1,1,3,1,1]
[(1,5),(2,7),(3,8),(4,6)] => [5,6,7,8,1,4,2,3] => [4,3,2,1,8,5,7,6] => [1,1,1,2,2,1]
[(1,4),(2,7),(3,8),(5,6)] => [4,6,7,1,8,5,2,3] => [5,3,2,8,1,4,7,6] => [1,1,2,3,1]
[(1,3),(2,7),(4,8),(5,6)] => [3,6,1,7,8,5,2,4] => [6,3,8,2,1,4,7,5] => [1,2,1,3,1]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,6,7,8,5,3,4] => [7,8,3,2,1,4,6,5] => [2,1,1,3,1]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [7,8,3,2,1,4,5,6] => [2,1,1,4]
[(1,3),(2,8),(4,7),(5,6)] => [3,6,1,7,8,5,4,2] => [6,3,8,2,1,4,5,7] => [1,2,1,4]
[(1,4),(2,8),(3,7),(5,6)] => [4,6,7,1,8,5,3,2] => [5,3,2,8,1,4,6,7] => [1,1,2,4]
[(1,5),(2,8),(3,7),(4,6)] => [5,6,7,8,1,4,3,2] => [4,3,2,1,8,5,6,7] => [1,1,1,2,3]
[(1,6),(2,8),(3,7),(4,5)] => [5,6,7,8,4,1,3,2] => [4,3,2,1,5,8,6,7] => [1,1,1,3,2]
[(1,7),(2,8),(3,6),(4,5)] => [5,6,7,8,4,3,1,2] => [4,3,2,1,5,6,8,7] => [1,1,1,4,1]
[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [4,3,2,1,5,6,7,8] => [1,1,1,5]
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [3,4,2,1,6,5,8,7,10,9] => [8,7,9,10,5,6,3,4,1,2] => [1,3,2,2,2]
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [3,5,2,6,4,1,8,7,10,9] => [8,6,9,5,7,10,3,4,1,2] => [1,2,3,2,2]
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [3,5,2,7,4,8,6,1,10,9] => [8,6,9,4,7,3,5,10,1,2] => [1,2,2,3,2]
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [3,5,2,7,4,9,6,10,8,1] => [8,6,9,4,7,2,5,1,3,10] => [1,2,2,2,3]
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,5,6,4,3,8,7,10,9] => [9,10,6,5,7,8,3,4,1,2] => [2,1,3,2,2]
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [4,5,6,3,2,1,8,7,10,9] => [7,6,5,8,9,10,3,4,1,2] => [1,1,4,2,2]
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [4,5,7,3,2,8,6,1,10,9] => [7,6,4,8,9,3,5,10,1,2] => [1,1,3,3,2]
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [4,5,7,3,2,9,6,10,8,1] => [7,6,4,8,9,2,5,1,3,10] => [1,1,3,2,3]
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,5,7,4,8,6,3,10,9] => [9,10,6,4,7,3,5,8,1,2] => [2,1,2,3,2]
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [4,6,7,3,8,5,2,1,10,9] => [7,5,4,8,3,6,9,10,1,2] => [1,1,2,4,2]
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [4,6,7,3,9,5,2,10,8,1] => [7,5,4,8,2,6,9,1,3,10] => [1,1,2,3,3]
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,5,7,4,9,6,10,8,3] => [9,10,6,4,7,2,5,1,3,8] => [2,1,2,2,3]
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [4,6,8,3,9,5,10,7,2,1] => [7,5,3,8,2,6,1,4,9,10] => [1,1,2,2,4]
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,7,8,6,5,10,9] => [9,10,7,8,4,3,5,6,1,2] => [2,2,1,3,2]
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [3,4,2,1,7,8,6,5,10,9] => [8,7,9,10,4,3,5,6,1,2] => [1,3,1,3,2]
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [3,6,2,7,8,5,4,1,10,9] => [8,5,9,4,3,6,7,10,1,2] => [1,2,1,4,2]
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [3,6,2,7,9,5,4,10,8,1] => [8,5,9,4,2,6,7,1,3,10] => [1,2,1,3,3]
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,6,7,8,5,4,3,10,9] => [9,10,5,4,3,6,7,8,1,2] => [2,1,1,4,2]
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [5,6,7,8,4,3,2,1,10,9] => [6,5,4,3,7,8,9,10,1,2] => [1,1,1,5,2]
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [5,6,7,9,4,3,2,10,8,1] => [6,5,4,2,7,8,9,1,3,10] => [1,1,1,4,3]
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,6,7,9,5,4,10,8,3] => [9,10,5,4,2,6,7,1,3,8] => [2,1,1,3,3]
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [5,6,8,9,4,3,10,7,2,1] => [6,5,3,2,7,8,1,4,9,10] => [1,1,1,3,4]
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,7,9,6,10,8,5] => [9,10,7,8,4,2,5,1,3,6] => [2,2,1,2,3]
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [3,4,2,1,7,9,6,10,8,5] => [8,7,9,10,4,2,5,1,3,6] => [1,3,1,2,3]
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [3,6,2,8,9,5,10,7,4,1] => [8,5,9,3,2,6,1,4,7,10] => [1,2,1,2,4]
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,6,8,9,5,10,7,4,3] => [9,10,5,3,2,6,1,4,7,8] => [2,1,1,2,4]
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [5,7,8,9,4,10,6,3,2,1] => [6,4,3,2,7,1,5,8,9,10] => [1,1,1,2,5]
[(1,7),(2,10),(3,9),(4,6),(5,8)] => [6,7,8,9,10,4,1,5,3,2] => [5,4,3,2,1,7,10,6,8,9] => [1,1,1,1,3,3]
[(1,5),(2,7),(3,8),(4,9),(6,10)] => [5,7,8,9,1,10,2,3,4,6] => [6,4,3,2,10,1,9,8,7,5] => [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] => [5,4,3,2,1,10,9,8,7,6] => [1,1,1,1,2,1,1,1,1]
[(1,10),(2,6),(3,7),(4,8),(5,9)] => [6,7,8,9,10,2,3,4,5,1] => [5,4,3,2,1,9,8,7,6,10] => [1,1,1,1,2,1,1,2]
[(1,4),(2,6),(3,8),(5,9),(7,10)] => [4,6,8,1,9,2,10,3,5,7] => [7,5,3,10,2,9,1,8,6,4] => [1,1,2,2,2,1,1]
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8] => [8,6,10,4,9,2,7,1,5,3] => [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] => [9,10,7,8,5,6,2,1,3,4] => [2,2,2,1,3]
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [3,4,2,1,6,5,9,10,8,7] => [8,7,9,10,5,6,2,1,3,4] => [1,3,2,1,3]
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [3,5,2,6,4,1,9,10,8,7] => [8,6,9,5,7,10,2,1,3,4] => [1,2,3,1,3]
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [3,5,2,8,4,9,10,7,6,1] => [8,6,9,3,7,2,1,4,5,10] => [1,2,2,1,4]
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,5,6,4,3,9,10,8,7] => [9,10,6,5,7,8,2,1,3,4] => [2,1,3,1,3]
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [4,5,6,3,2,1,9,10,8,7] => [7,6,5,8,9,10,2,1,3,4] => [1,1,4,1,3]
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [4,5,8,3,2,9,10,7,6,1] => [7,6,3,8,9,2,1,4,5,10] => [1,1,3,1,4]
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,5,8,4,9,10,7,6,3] => [9,10,6,3,7,2,1,4,5,8] => [2,1,2,1,4]
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [4,7,8,3,9,10,6,5,2,1] => [7,4,3,8,2,1,5,6,9,10] => [1,1,2,1,5]
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,8,9,10,7,6,5] => [9,10,7,8,3,2,1,4,5,6] => [2,2,1,1,4]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [3,4,2,1,8,9,10,7,6,5] => [8,7,9,10,3,2,1,4,5,6] => [1,3,1,1,4]
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [3,7,2,8,9,10,6,5,4,1] => [8,4,9,3,2,1,5,6,7,10] => [1,2,1,1,5]
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,7,8,9,10,6,5,4,3] => [9,10,4,3,2,1,5,6,7,8] => [2,1,1,1,5]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [6,7,8,9,10,5,4,3,2,1] => [5,4,3,2,1,6,7,8,9,10] => [1,1,1,1,6]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [7,8,9,10,11,12,6,5,4,3,2,1] => [6,5,4,3,2,1,7,8,9,10,11,12] => [1,1,1,1,1,7]
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,7,8,9,10,6,5,4,3,12,11] => [11,12,6,5,4,3,7,8,9,10,1,2] => [2,1,1,1,5,2]
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [3,7,2,8,9,11,6,5,4,12,10,1] => [10,6,11,5,4,2,7,8,9,1,3,12] => [1,2,1,1,4,3]
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,7,8,9,11,6,5,4,12,10,3] => [11,12,6,5,4,2,7,8,9,1,3,10] => [2,1,1,1,4,3]
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [3,7,2,8,9,10,6,5,4,1,12,11] => [10,6,11,5,4,3,7,8,9,12,1,2] => [1,2,1,1,5,2]
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [4,7,8,3,10,11,6,5,12,9,2,1] => [9,6,5,10,3,2,7,8,1,4,11,12] => [1,1,2,1,3,4]
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,7,8,6,5,10,9,12,11] => [11,12,9,10,6,5,7,8,3,4,1,2] => [2,2,1,3,2,2]
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [3,7,2,8,10,11,6,5,12,9,4,1] => [10,6,11,5,3,2,7,8,1,4,9,12] => [1,2,1,1,3,4]
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,7,8,10,11,6,5,12,9,4,3] => [11,12,6,5,3,2,7,8,1,4,9,10] => [2,1,1,1,3,4]
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [3,4,2,1,7,8,6,5,10,9,12,11] => [10,9,11,12,6,5,7,8,3,4,1,2] => [1,3,1,3,2,2]
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [4,7,8,3,9,11,6,5,2,12,10,1] => [9,6,5,10,4,2,7,8,11,1,3,12] => [1,1,2,1,4,3]
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,7,8,6,5,11,12,10,9] => [11,12,9,10,6,5,7,8,2,1,3,4] => [2,2,1,3,1,3]
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [4,7,8,3,9,10,6,5,2,1,12,11] => [9,6,5,10,4,3,7,8,11,12,1,2] => [1,1,2,1,5,2]
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [3,4,2,1,7,8,6,5,11,12,10,9] => [10,9,11,12,6,5,7,8,2,1,3,4] => [1,3,1,3,1,3]
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [5,7,9,10,4,11,6,12,8,3,2,1] => [8,6,4,3,9,2,7,1,5,10,11,12] => [1,1,1,2,2,5]
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,5,7,4,9,6,10,8,3,12,11] => [11,12,8,6,9,4,7,3,5,10,1,2] => [2,1,2,2,3,2]
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [3,5,2,7,4,9,6,11,8,12,10,1] => [10,8,11,6,9,4,7,2,5,1,3,12] => [1,2,2,2,2,3]
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,5,7,4,9,6,11,8,12,10,3] => [11,12,8,6,9,4,7,2,5,1,3,10] => [2,1,2,2,2,3]
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [3,5,2,7,4,9,6,10,8,1,12,11] => [10,8,11,6,9,4,7,3,5,12,1,2] => [1,2,2,2,3,2]
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [4,7,9,3,10,11,6,12,8,5,2,1] => [9,6,4,10,3,2,7,1,5,8,11,12] => [1,1,2,1,2,5]
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,7,9,6,10,8,5,12,11] => [11,12,9,10,6,4,7,3,5,8,1,2] => [2,2,1,2,3,2]
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [3,7,2,9,10,11,6,12,8,5,4,1] => [10,6,11,4,3,2,7,1,5,8,9,12] => [1,2,1,1,2,5]
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,7,9,10,11,6,12,8,5,4,3] => [11,12,6,4,3,2,7,1,5,8,9,10] => [2,1,1,1,2,5]
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [3,4,2,1,7,9,6,10,8,5,12,11] => [10,9,11,12,6,4,7,3,5,8,1,2] => [1,3,1,2,3,2]
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [4,5,7,3,2,9,6,11,8,12,10,1] => [9,8,6,10,11,4,7,2,5,1,3,12] => [1,1,3,2,2,3]
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,7,9,6,11,8,12,10,5] => [11,12,9,10,6,4,7,2,5,1,3,8] => [2,2,1,2,2,3]
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [4,5,7,3,2,9,6,10,8,1,12,11] => [9,8,6,10,11,4,7,3,5,12,1,2] => [1,1,3,2,3,2]
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [3,4,2,1,7,9,6,11,8,12,10,5] => [10,9,11,12,6,4,7,2,5,1,3,8] => [1,3,1,2,2,3]
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [5,7,8,10,4,11,6,3,12,9,2,1] => [8,6,5,3,9,2,7,10,1,4,11,12] => [1,1,1,2,3,4]
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,5,7,4,8,6,3,10,9,12,11] => [11,12,8,6,9,5,7,10,3,4,1,2] => [2,1,2,3,2,2]
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [3,5,2,7,4,10,6,11,12,9,8,1] => [10,8,11,6,9,3,7,2,1,4,5,12] => [1,2,2,2,1,4]
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,5,7,4,10,6,11,12,9,8,3] => [11,12,8,6,9,3,7,2,1,4,5,10] => [2,1,2,2,1,4]
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [3,5,2,7,4,8,6,1,10,9,12,11] => [10,8,11,6,9,5,7,12,3,4,1,2] => [1,2,2,3,2,2]
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [5,7,8,9,4,11,6,3,2,12,10,1] => [8,6,5,4,9,2,7,10,11,1,3,12] => [1,1,1,2,4,3]
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,5,7,4,8,6,3,11,12,10,9] => [11,12,8,6,9,5,7,10,2,1,3,4] => [2,1,2,3,1,3]
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [5,7,8,9,4,10,6,3,2,1,12,11] => [8,6,5,4,9,3,7,10,11,12,1,2] => [1,1,1,2,5,2]
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [3,5,2,7,4,8,6,1,11,12,10,9] => [10,8,11,6,9,5,7,12,2,1,3,4] => [1,2,2,3,1,3]
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [4,5,7,3,2,10,6,11,12,9,8,1] => [9,8,6,10,11,3,7,2,1,4,5,12] => [1,1,3,2,1,4]
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,7,10,6,11,12,9,8,5] => [11,12,9,10,6,3,7,2,1,4,5,8] => [2,2,1,2,1,4]
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [4,5,7,3,2,8,6,1,10,9,12,11] => [9,8,6,10,11,5,7,12,3,4,1,2] => [1,1,3,3,2,2]
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [3,4,2,1,7,10,6,11,12,9,8,5] => [10,9,11,12,6,3,7,2,1,4,5,8] => [1,3,1,2,1,4]
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [4,5,7,3,2,8,6,1,11,12,10,9] => [9,8,6,10,11,5,7,12,2,1,3,4] => [1,1,3,3,1,3]
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [6,8,9,10,11,5,12,7,4,3,2,1] => [7,5,4,3,2,8,1,6,9,10,11,12] => [1,1,1,1,2,6]
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,6,8,9,5,10,7,4,3,12,11] => [11,12,7,5,4,8,3,6,9,10,1,2] => [2,1,1,2,4,2]
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [3,6,2,8,9,5,11,7,4,12,10,1] => [10,7,11,5,4,8,2,6,9,1,3,12] => [1,2,1,2,3,3]
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,6,8,9,5,11,7,4,12,10,3] => [11,12,7,5,4,8,2,6,9,1,3,10] => [2,1,1,2,3,3]
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [3,6,2,8,9,5,10,7,4,1,12,11] => [10,7,11,5,4,8,3,6,9,12,1,2] => [1,2,1,2,4,2]
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [4,6,8,3,10,5,11,7,12,9,2,1] => [9,7,5,10,3,8,2,6,1,4,11,12] => [1,1,2,2,2,4]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,2,2,2,2,2]
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [3,6,2,8,10,5,11,7,12,9,4,1] => [10,7,11,5,3,8,2,6,1,4,9,12] => [1,2,1,2,2,4]
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,6,8,10,5,11,7,12,9,4,3] => [11,12,7,5,3,8,2,6,1,4,9,10] => [2,1,1,2,2,4]
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [3,4,2,1,6,5,8,7,10,9,12,11] => [10,9,11,12,7,8,5,6,3,4,1,2] => [1,3,2,2,2,2]
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [4,6,8,3,9,5,11,7,2,12,10,1] => [9,7,5,10,4,8,2,6,11,1,3,12] => [1,1,2,2,3,3]
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,11,12,10,9] => [11,12,9,10,7,8,5,6,2,1,3,4] => [2,2,2,2,1,3]
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [4,6,8,3,9,5,10,7,2,1,12,11] => [9,7,5,10,4,8,3,6,11,12,1,2] => [1,1,2,2,4,2]
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [3,4,2,1,6,5,8,7,11,12,10,9] => [10,9,11,12,7,8,5,6,2,1,3,4] => [1,3,2,2,1,3]
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [5,8,9,10,4,11,12,7,6,3,2,1] => [8,5,4,3,9,2,1,6,7,10,11,12] => [1,1,1,2,1,6]
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,5,8,4,9,10,7,6,3,12,11] => [11,12,8,5,9,4,3,6,7,10,1,2] => [2,1,2,1,4,2]
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [3,5,2,8,4,9,11,7,6,12,10,1] => [10,8,11,5,9,4,2,6,7,1,3,12] => [1,2,2,1,3,3]
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,5,8,4,9,11,7,6,12,10,3] => [11,12,8,5,9,4,2,6,7,1,3,10] => [2,1,2,1,3,3]
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [3,5,2,8,4,9,10,7,6,1,12,11] => [10,8,11,5,9,4,3,6,7,12,1,2] => [1,2,2,1,4,2]
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [4,8,9,3,10,11,12,7,6,5,2,1] => [9,5,4,10,3,2,1,6,7,8,11,12] => [1,1,2,1,1,6]
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,8,9,10,7,6,5,12,11] => [11,12,9,10,5,4,3,6,7,8,1,2] => [2,2,1,1,4,2]
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [3,8,2,9,10,11,12,7,6,5,4,1] => [10,5,11,4,3,2,1,6,7,8,9,12] => [1,2,1,1,1,6]
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,8,9,10,11,12,7,6,5,4,3] => [11,12,5,4,3,2,1,6,7,8,9,10] => [2,1,1,1,1,6]
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [3,4,2,1,8,9,10,7,6,5,12,11] => [10,9,11,12,5,4,3,6,7,8,1,2] => [1,3,1,1,4,2]
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [4,5,8,3,2,9,11,7,6,12,10,1] => [9,8,5,10,11,4,2,6,7,1,3,12] => [1,1,3,1,3,3]
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,8,9,11,7,6,12,10,5] => [11,12,9,10,5,4,2,6,7,1,3,8] => [2,2,1,1,3,3]
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [4,5,8,3,2,9,10,7,6,1,12,11] => [9,8,5,10,11,4,3,6,7,12,1,2] => [1,1,3,1,4,2]
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [3,4,2,1,8,9,11,7,6,12,10,5] => [10,9,11,12,5,4,2,6,7,1,3,8] => [1,3,1,1,3,3]
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [5,6,8,10,4,3,11,7,12,9,2,1] => [8,7,5,3,9,10,2,6,1,4,11,12] => [1,1,1,3,2,4]
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,5,6,4,3,8,7,10,9,12,11] => [11,12,8,7,9,10,5,6,3,4,1,2] => [2,1,3,2,2,2]
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [3,5,2,8,4,10,11,7,12,9,6,1] => [10,8,11,5,9,3,2,6,1,4,7,12] => [1,2,2,1,2,4]
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,5,8,4,10,11,7,12,9,6,3] => [11,12,8,5,9,3,2,6,1,4,7,10] => [2,1,2,1,2,4]
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [3,5,2,6,4,1,8,7,10,9,12,11] => [10,8,11,7,9,12,5,6,3,4,1,2] => [1,2,3,2,2,2]
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [5,6,8,9,4,3,11,7,2,12,10,1] => [8,7,5,4,9,10,2,6,11,1,3,12] => [1,1,1,3,3,3]
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,5,6,4,3,8,7,11,12,10,9] => [11,12,8,7,9,10,5,6,2,1,3,4] => [2,1,3,2,1,3]
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [5,6,8,9,4,3,10,7,2,1,12,11] => [8,7,5,4,9,10,3,6,11,12,1,2] => [1,1,1,3,4,2]
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [3,5,2,6,4,1,8,7,11,12,10,9] => [10,8,11,7,9,12,5,6,2,1,3,4] => [1,2,3,2,1,3]
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [4,5,8,3,2,10,11,7,12,9,6,1] => [9,8,5,10,11,3,2,6,1,4,7,12] => [1,1,3,1,2,4]
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,8,10,11,7,12,9,6,5] => [11,12,9,10,5,3,2,6,1,4,7,8] => [2,2,1,1,2,4]
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [4,5,6,3,2,1,8,7,10,9,12,11] => [9,8,7,10,11,12,5,6,3,4,1,2] => [1,1,4,2,2,2]
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [3,4,2,1,8,10,11,7,12,9,6,5] => [10,9,11,12,5,3,2,6,1,4,7,8] => [1,3,1,1,2,4]
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [4,5,6,3,2,1,8,7,11,12,10,9] => [9,8,7,10,11,12,5,6,2,1,3,4] => [1,1,4,2,1,3]
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [6,7,9,10,11,5,4,12,8,3,2,1] => [7,6,4,3,2,8,9,1,5,10,11,12] => [1,1,1,1,3,5]
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,6,7,9,5,4,10,8,3,12,11] => [11,12,7,6,4,8,9,3,5,10,1,2] => [2,1,1,3,3,2]
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [3,6,2,7,9,5,4,11,8,12,10,1] => [10,7,11,6,4,8,9,2,5,1,3,12] => [1,2,1,3,2,3]
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,6,7,9,5,4,11,8,12,10,3] => [11,12,7,6,4,8,9,2,5,1,3,10] => [2,1,1,3,2,3]
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [3,6,2,7,9,5,4,10,8,1,12,11] => [10,7,11,6,4,8,9,3,5,12,1,2] => [1,2,1,3,3,2]
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [4,6,9,3,10,5,11,12,8,7,2,1] => [9,7,4,10,3,8,2,1,5,6,11,12] => [1,1,2,2,1,5]
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,9,10,8,7,12,11] => [11,12,9,10,7,8,4,3,5,6,1,2] => [2,2,2,1,3,2]
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [3,6,2,9,10,5,11,12,8,7,4,1] => [10,7,11,4,3,8,2,1,5,6,9,12] => [1,2,1,2,1,5]
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,6,9,10,5,11,12,8,7,4,3] => [11,12,7,4,3,8,2,1,5,6,9,10] => [2,1,1,2,1,5]
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [3,4,2,1,6,5,9,10,8,7,12,11] => [10,9,11,12,7,8,4,3,5,6,1,2] => [1,3,2,1,3,2]
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [4,6,7,3,9,5,2,11,8,12,10,1] => [9,7,6,10,4,8,11,2,5,1,3,12] => [1,1,2,3,2,3]
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,9,11,8,12,10,7] => [11,12,9,10,7,8,4,2,5,1,3,6] => [2,2,2,1,2,3]
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [4,6,7,3,9,5,2,10,8,1,12,11] => [9,7,6,10,4,8,11,3,5,12,1,2] => [1,1,2,3,3,2]
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [3,4,2,1,6,5,9,11,8,12,10,7] => [10,9,11,12,7,8,4,2,5,1,3,6] => [1,3,2,1,2,3]
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [6,7,8,10,11,5,4,3,12,9,2,1] => [7,6,5,3,2,8,9,10,1,4,11,12] => [1,1,1,1,4,4]
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,6,7,8,5,4,3,10,9,12,11] => [11,12,7,6,5,8,9,10,3,4,1,2] => [2,1,1,4,2,2]
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [3,6,2,7,10,5,4,11,12,9,8,1] => [10,7,11,6,3,8,9,2,1,4,5,12] => [1,2,1,3,1,4]
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,6,7,10,5,4,11,12,9,8,3] => [11,12,7,6,3,8,9,2,1,4,5,10] => [2,1,1,3,1,4]
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [3,6,2,7,8,5,4,1,10,9,12,11] => [10,7,11,6,5,8,9,12,3,4,1,2] => [1,2,1,4,2,2]
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [6,7,8,9,11,5,4,3,2,12,10,1] => [7,6,5,4,2,8,9,10,11,1,3,12] => [1,1,1,1,5,3]
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,6,7,8,5,4,3,11,12,10,9] => [11,12,7,6,5,8,9,10,2,1,3,4] => [2,1,1,4,1,3]
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [6,7,8,9,10,5,4,3,2,1,12,11] => [7,6,5,4,3,8,9,10,11,12,1,2] => [1,1,1,1,6,2]
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [3,6,2,7,8,5,4,1,11,12,10,9] => [10,7,11,6,5,8,9,12,2,1,3,4] => [1,2,1,4,1,3]
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [4,6,7,3,10,5,2,11,12,9,8,1] => [9,7,6,10,3,8,11,2,1,4,5,12] => [1,1,2,3,1,4]
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,10,11,12,9,8,7] => [11,12,9,10,7,8,3,2,1,4,5,6] => [2,2,2,1,1,4]
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [4,6,7,3,8,5,2,1,10,9,12,11] => [9,7,6,10,5,8,11,12,3,4,1,2] => [1,1,2,4,2,2]
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [3,4,2,1,6,5,10,11,12,9,8,7] => [10,9,11,12,7,8,3,2,1,4,5,6] => [1,3,2,1,1,4]
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [4,6,7,3,8,5,2,1,11,12,10,9] => [9,7,6,10,5,8,11,12,2,1,3,4] => [1,1,2,4,1,3]
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [5,6,9,10,4,3,11,12,8,7,2,1] => [8,7,4,3,9,10,2,1,5,6,11,12] => [1,1,1,3,1,5]
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,5,6,4,3,9,10,8,7,12,11] => [11,12,8,7,9,10,4,3,5,6,1,2] => [2,1,3,1,3,2]
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [3,5,2,9,4,10,11,12,8,7,6,1] => [10,8,11,4,9,3,2,1,5,6,7,12] => [1,2,2,1,1,5]
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,5,9,4,10,11,12,8,7,6,3] => [11,12,8,4,9,3,2,1,5,6,7,10] => [2,1,2,1,1,5]
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [3,5,2,6,4,1,9,10,8,7,12,11] => [10,8,11,7,9,12,4,3,5,6,1,2] => [1,2,3,1,3,2]
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [5,6,7,9,4,3,2,11,8,12,10,1] => [8,7,6,4,9,10,11,2,5,1,3,12] => [1,1,1,4,2,3]
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,5,6,4,3,9,11,8,12,10,7] => [11,12,8,7,9,10,4,2,5,1,3,6] => [2,1,3,1,2,3]
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [5,6,7,9,4,3,2,10,8,1,12,11] => [8,7,6,4,9,10,11,3,5,12,1,2] => [1,1,1,4,3,2]
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [3,5,2,6,4,1,9,11,8,12,10,7] => [10,8,11,7,9,12,4,2,5,1,3,6] => [1,2,3,1,2,3]
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [4,5,9,3,2,10,11,12,8,7,6,1] => [9,8,4,10,11,3,2,1,5,6,7,12] => [1,1,3,1,1,5]
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,9,10,11,12,8,7,6,5] => [11,12,9,10,4,3,2,1,5,6,7,8] => [2,2,1,1,1,5]
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [4,5,6,3,2,1,9,10,8,7,12,11] => [9,8,7,10,11,12,4,3,5,6,1,2] => [1,1,4,1,3,2]
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [3,4,2,1,9,10,11,12,8,7,6,5] => [10,9,11,12,4,3,2,1,5,6,7,8] => [1,3,1,1,1,5]
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [4,5,6,3,2,1,9,11,8,12,10,7] => [9,8,7,10,11,12,4,2,5,1,3,6] => [1,1,4,1,2,3]
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [5,6,7,10,4,3,2,11,12,9,8,1] => [8,7,6,3,9,10,11,2,1,4,5,12] => [1,1,1,4,1,4]
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,5,6,4,3,10,11,12,9,8,7] => [11,12,8,7,9,10,3,2,1,4,5,6] => [2,1,3,1,1,4]
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [5,6,7,8,4,3,2,1,10,9,12,11] => [8,7,6,5,9,10,11,12,3,4,1,2] => [1,1,1,5,2,2]
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [3,5,2,6,4,1,10,11,12,9,8,7] => [10,8,11,7,9,12,3,2,1,4,5,6] => [1,2,3,1,1,4]
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [5,6,7,8,4,3,2,1,11,12,10,9] => [8,7,6,5,9,10,11,12,2,1,3,4] => [1,1,1,5,1,3]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [4,5,6,3,2,1,10,11,12,9,8,7] => [9,8,7,10,11,12,3,2,1,4,5,6] => [1,1,4,1,1,4]
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [9,8,7,12,11,10,3,2,1,6,5,4] => [1,1,2,1,1,1,1,2,1,1]
[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => [5,6,9,10,1,2,11,12,3,4,7,8] => [8,7,4,3,12,11,2,1,10,9,6,5] => [1,1,1,2,1,1,2,1,1,1]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [6,5,4,3,2,1,12,11,10,9,8,7] => [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
complement
Description
Sents a permutation to its complement.
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.