Identifier
Mp00058: Perfect matchings to permutationPermutations
Mp00235: Permutations descent views to invisible inversion bottomsPermutations
Mp00067: Permutations Foata bijectionPermutations
Images
[(1,2)] => [2,1] => [2,1] => [2,1]
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [4,2,1,3]
[(1,3),(2,4)] => [3,4,1,2] => [4,1,3,2] => [4,1,3,2]
[(1,4),(2,3)] => [4,3,2,1] => [2,3,4,1] => [2,3,4,1]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [6,4,2,1,3,5]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => [6,4,1,3,2,5]
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => [6,2,3,4,1,5]
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => [1,3,2,6,5,4]
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [4,3,5,6,1,2] => [1,4,3,5,6,2]
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [3,5,2,6,4,1] => [5,3,6,2,4,1]
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [2,6,1,5,4,3] => [6,5,2,1,4,3]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,1,2,6,5,3]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [5,6,3,2,1,4] => [3,5,6,2,1,4]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => [6,2,5,1,3,4]
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => [4,2,1,5,6,3]
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [6,4,3,5,1,2] => [1,4,6,3,5,2]
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [5,3,1,4,6,2] => [3,5,4,1,6,2]
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [3,1,4,6,5,2] => [6,3,4,1,5,2]
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [2,3,4,5,6,1]
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [8,6,4,2,1,3,5,7]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => [8,6,4,1,3,2,5,7]
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [8,6,2,3,4,1,5,7]
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [6,3,5,1,2,4,8,7] => [8,1,3,2,6,5,4,7]
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [4,3,5,6,1,2,8,7] => [8,1,4,3,5,6,2,7]
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [8,3,7,5,2,1,4,6] => [3,2,8,5,7,1,4,6]
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [6,3,7,5,1,8,4,2] => [6,7,5,3,8,4,1,2]
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [6,5,2,7,1,8,3,4] => [2,6,5,7,1,8,3,4]
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [8,5,2,7,4,1,3,6] => [2,5,1,8,7,4,3,6]
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [3,5,2,6,4,1,8,7] => [8,5,3,6,2,4,1,7]
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [2,6,1,5,4,3,8,7] => [8,6,5,2,1,4,3,7]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [6,1,2,4,5,3,8,7] => [8,4,1,2,6,5,3,7]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [5,6,3,2,1,4,8,7] => [8,3,5,6,2,1,4,7]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => [8,6,2,5,1,3,4,7]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => [8,4,2,1,5,6,3,7]
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [6,4,3,5,1,2,8,7] => [8,1,4,6,3,5,2,7]
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [5,3,1,4,6,2,8,7] => [8,3,5,4,1,6,2,7]
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [3,1,4,6,5,2,8,7] => [8,6,3,4,1,5,2,7]
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => [8,2,3,4,5,6,1,7]
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [8,3,4,5,7,1,2,6] => [1,3,4,5,2,8,7,6]
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [6,3,4,5,7,8,1,2] => [1,3,4,6,5,7,8,2]
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [5,7,4,6,2,8,3,1] => [5,4,7,6,8,2,3,1]
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [2,8,4,6,1,7,3,5] => [4,2,1,8,6,7,3,5]
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [8,1,4,7,2,6,3,5] => [4,1,8,2,3,7,6,5]
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [3,4,7,8,5,2,1,6] => [3,7,4,5,8,2,1,6]
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [5,7,2,4,8,1,3,6] => [2,1,5,4,7,3,8,6]
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [7,8,3,5,1,2,4,6] => [1,3,2,5,7,8,4,6]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,8,5,7,3,4,6] => [2,1,8,5,3,4,7,6]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,6,5,7,8,3,4] => [2,6,5,1,3,7,8,4]
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [8,6,3,5,1,7,4,2] => [6,3,8,5,7,4,1,2]
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [5,8,2,4,6,7,3,1] => [5,2,4,6,8,7,3,1]
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [3,4,8,6,5,7,1,2] => [1,6,8,3,4,5,7,2]
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [7,5,4,8,1,6,3,2] => [5,7,4,8,6,1,3,2]
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [5,1,4,6,8,2,7,3] => [5,4,1,6,8,2,7,3]
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [2,5,4,6,7,1,8,3] => [5,4,2,6,7,8,1,3]
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [2,4,6,3,7,5,8,1] => [6,4,2,7,3,5,8,1]
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [4,1,6,3,8,5,7,2] => [6,4,8,1,3,5,7,2]
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [3,7,4,2,8,6,5,1] => [7,8,6,3,4,2,5,1]
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [7,4,1,3,5,8,6,2] => [7,4,1,8,3,5,6,2]
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [6,5,8,4,1,7,3,2] => [6,5,4,8,7,3,1,2]
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [8,5,3,7,4,1,6,2] => [5,3,8,7,4,6,1,2]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,5,7,4,8,6,3] => [7,5,8,2,1,4,6,3]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,4,8,3,7,6,5] => [8,7,4,2,1,3,6,5]
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [7,4,3,8,2,1,6,5] => [7,4,8,3,2,6,1,5]
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [6,3,7,4,1,8,2,5] => [3,6,7,4,1,8,2,5]
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [8,3,1,2,5,7,6,4] => [8,7,1,3,2,5,6,4]
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [3,1,8,2,7,6,5,4] => [8,7,6,3,1,5,2,4]
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [2,3,8,1,6,7,5,4] => [6,8,2,3,1,7,5,4]
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [4,3,7,2,6,8,5,1] => [7,4,3,2,6,8,5,1]
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [4,7,2,3,8,5,6,1] => [2,7,4,3,8,5,6,1]
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [3,8,2,1,7,5,6,4] => [8,3,7,2,1,5,6,4]
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [2,8,1,3,6,5,7,4] => [8,2,6,1,3,5,7,4]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => [5,1,2,3,6,8,7,4]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [7,8,2,4,3,6,1,5] => [2,4,7,3,8,1,6,5]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [6,8,3,2,4,1,7,5] => [6,3,8,2,7,4,1,5]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,8,3,4,6,7,5] => [8,2,1,3,6,4,7,5]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,4,3,6] => [5,7,8,2,1,4,3,6]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,4,2,6] => [3,5,1,7,8,4,2,6]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [7,1,8,4,5,3,2,6] => [1,7,8,4,5,3,2,6]
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [2,7,8,5,4,3,1,6] => [5,7,8,2,4,3,1,6]
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [8,7,1,6,3,4,2,5] => [1,8,3,4,7,6,2,5]
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [3,8,6,7,2,4,1,5] => [3,2,4,8,6,7,1,5]
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [5,6,7,8,3,4,2,1] => [3,5,6,7,8,4,2,1]
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [5,3,8,7,4,2,6,1] => [5,8,3,7,4,2,6,1]
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [4,3,8,7,2,1,6,5] => [8,4,7,3,2,6,1,5]
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [8,3,6,1,4,2,7,5] => [8,3,1,6,7,4,2,5]
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [7,3,5,8,2,4,1,6] => [3,2,5,7,4,8,1,6]
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [2,3,4,1,8,5,7,6] => [8,2,7,3,4,1,5,6]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => [8,4,7,1,3,2,5,6]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,5,7,6] => [8,4,7,2,1,3,5,6]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => [6,4,2,1,3,7,8,5]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [4,1,3,2,6,7,8,5] => [6,4,1,3,2,7,8,5]
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => [6,2,3,4,1,7,8,5]
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [8,3,5,6,2,7,1,4] => [3,2,5,6,8,1,7,4]
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [7,3,6,5,1,2,8,4] => [7,1,6,3,5,8,2,4]
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [5,3,6,1,8,7,2,4] => [3,8,5,1,6,7,2,4]
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [4,3,5,6,7,8,1,2] => [1,4,3,5,6,7,8,2]
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [3,5,6,7,8,4,2,1] => [5,3,6,7,8,4,2,1]
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [5,6,2,8,7,4,1,3] => [2,8,5,6,7,1,4,3]
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [7,8,5,6,1,4,2,3] => [1,5,2,7,8,6,4,3]
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [2,8,6,5,4,7,1,3] => [2,6,8,5,1,4,7,3]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [8,1,6,4,5,7,2,3] => [1,4,2,8,6,5,7,3]
>>> Load all 357 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [5,8,3,6,1,7,2,4] => [3,5,1,6,8,7,2,4]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,8,6,5,7,3,4] => [2,6,8,5,1,3,7,4]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,7,5,3,6,8,4] => [5,7,6,2,1,3,8,4]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [6,7,3,5,2,1,8,4] => [6,3,7,5,8,2,1,4]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [8,7,5,4,2,6,1,3] => [2,5,8,7,4,1,6,3]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [7,1,4,2,5,6,8,3] => [4,1,7,5,2,6,8,3]
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [2,7,4,1,6,5,8,3] => [7,6,2,4,5,1,8,3]
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [4,6,1,2,8,7,3,5] => [4,8,1,2,6,7,3,5]
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [3,4,6,1,7,8,2,5] => [3,4,1,6,7,2,8,5]
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [3,4,2,5,7,8,6,1] => [7,3,4,2,5,8,6,1]
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [2,4,1,5,8,7,6,3] => [8,7,4,2,5,1,6,3]
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [4,1,2,5,8,6,7,3] => [8,1,4,5,2,6,7,3]
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [6,4,2,1,5,8,7,3] => [8,4,6,5,2,1,7,3]
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [8,5,2,4,6,1,7,3] => [5,2,4,8,6,7,1,3]
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [7,5,3,2,6,8,1,4] => [3,5,7,2,1,6,8,4]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,5,3,6,8,7,4] => [8,5,6,2,1,3,7,4]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => [4,2,1,5,6,7,8,3]
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [8,4,3,5,6,7,1,2] => [1,4,3,5,8,6,7,2]
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [7,3,5,4,6,1,8,2] => [3,7,5,4,6,8,1,2]
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [6,3,4,1,5,7,8,2] => [3,4,6,5,1,7,8,2]
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [4,3,1,5,7,6,8,2] => [7,4,3,5,1,6,8,2]
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [3,1,4,5,6,8,7,2] => [8,3,4,1,5,6,7,2]
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1]
[(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] => [10,8,6,4,2,1,3,5,7,9]
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [4,1,3,2,6,5,8,7,10,9] => [10,8,6,4,1,3,2,5,7,9]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => [10,8,6,2,3,4,1,5,7,9]
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [4,3,5,6,1,2,8,7,10,9] => [10,8,1,4,3,5,6,2,7,9]
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [6,3,7,5,1,8,4,2,10,9] => [10,6,7,5,3,8,4,1,2,9]
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [8,3,9,5,1,7,4,10,6,2] => [8,9,3,7,5,10,4,1,6,2]
[(1,6),(2,4),(3,5),(7,8),(9,10)] => [6,4,5,2,3,1,8,7,10,9] => [3,5,2,6,4,1,8,7,10,9] => [10,8,5,3,6,2,4,1,7,9]
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [6,1,2,4,5,3,8,7,10,9] => [10,8,4,1,2,6,5,3,7,9]
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,6,3,5,4,8,7,10,9] => [10,8,6,2,5,1,3,4,7,9]
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,4,5,6,3,8,7,10,9] => [10,8,4,2,1,5,6,3,7,9]
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [2,3,4,5,6,1,8,7,10,9] => [10,8,2,3,4,5,6,1,7,9]
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [6,3,4,5,7,8,1,2,10,9] => [10,1,3,4,6,5,7,8,2,9]
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [8,3,4,5,9,7,1,10,6,2] => [8,9,3,4,7,5,10,6,1,2]
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [2,1,6,5,7,8,3,4,10,9] => [10,2,6,5,1,3,7,8,4,9]
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [2,5,4,6,7,1,8,3,10,9] => [10,5,4,2,6,7,8,1,3,9]
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [8,5,4,6,7,1,9,10,3,2] => [5,4,8,6,7,9,10,1,3,2]
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [2,1,8,5,9,7,3,10,6,4] => [8,9,7,5,10,2,1,6,3,4]
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [2,7,4,8,6,1,9,5,10,3] => [7,8,6,4,2,9,5,1,10,3]
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => [10,1,6,3,9,5,2,8,4,7] => [6,1,10,9,3,5,2,8,4,7]
[(1,2),(3,8),(4,6),(5,7),(9,10)] => [2,1,8,6,7,4,5,3,10,9] => [2,1,5,7,4,8,6,3,10,9] => [10,7,5,8,2,1,4,6,3,9]
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [8,1,2,3,5,6,7,4,10,9] => [10,5,1,2,3,6,8,7,4,9]
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,8,3,4,6,7,5,10,9] => [10,8,2,1,3,6,4,7,5,9]
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [4,1,3,2,8,5,7,6,10,9] => [10,8,4,7,1,3,2,5,6,9]
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,8,5,7,6,10,9] => [10,8,4,7,2,1,3,5,6,9]
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,6,7,8,5,10,9] => [10,6,4,2,1,3,7,8,5,9]
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9] => [10,6,2,3,4,1,7,8,5,9]
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [4,3,5,6,7,8,1,2,10,9] => [10,1,4,3,5,6,7,8,2,9]
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [8,3,9,5,6,7,1,10,4,2] => [5,3,8,9,6,7,10,4,1,2]
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9] => [10,4,2,1,5,6,7,8,3,9]
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9] => [10,2,3,4,5,6,7,8,1,9]
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [10,3,4,5,6,7,9,1,2,8] => [1,3,4,5,6,7,2,10,9,8]
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [8,3,4,5,6,7,9,10,1,2] => [1,3,4,5,6,8,7,9,10,2]
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [2,1,8,5,6,7,9,10,3,4] => [2,8,1,3,5,6,7,9,10,4]
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [2,7,4,5,6,8,9,1,10,3] => [4,2,7,5,6,8,9,10,1,3]
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [2,1,4,3,8,7,9,10,5,6] => [4,8,7,2,1,3,5,9,10,6]
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [2,3,4,1,8,7,9,10,5,6] => [2,8,7,3,4,1,5,9,10,6]
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [4,3,7,8,6,10,9,2,5,1] => [4,10,7,3,2,8,6,9,5,1]
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,4,7,6,8,9,3,10,5] => [7,6,4,2,1,8,9,10,3,5]
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [2,3,6,5,7,8,1,9,10,4] => [6,5,2,3,7,8,9,1,10,4]
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [3,5,2,7,4,9,6,10,8,1] => [9,7,5,3,10,2,4,6,8,1]
[(1,2),(3,4),(5,10),(6,8),(7,9)] => [2,1,4,3,10,8,9,6,7,5] => [2,1,4,3,7,9,6,10,8,5] => [9,7,10,4,2,1,3,6,8,5]
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,3,4,5,7,8,9,6] => [10,2,1,3,4,5,7,8,9,6]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => [6,1,2,3,4,7,8,10,9,5]
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => [10,3,7,1,4,5,2,8,9,6] => [7,3,4,1,10,5,8,2,9,6]
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [4,1,3,2,10,5,6,8,9,7] => [10,4,1,3,8,2,5,6,9,7]
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,10,5,6,8,9,7] => [10,4,2,1,8,3,5,6,9,7]
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => [10,3,4,5,8,1,6,2,9,7] => [10,3,4,5,1,8,9,6,2,7]
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,6,3,5,4,10,7,9,8] => [10,6,9,2,5,1,3,4,7,8]
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [6,1,2,4,5,3,10,7,9,8] => [10,4,9,1,2,6,5,3,7,8]
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [4,1,3,2,6,5,10,7,9,8] => [10,6,9,4,1,3,2,5,7,8]
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,10,7,9,8] => [10,6,9,4,2,1,3,5,7,8]
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,8,9,10,7] => [8,6,4,2,1,3,5,9,10,7]
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7] => [8,6,2,3,4,1,5,9,10,7]
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [4,3,5,6,1,2,8,9,10,7] => [8,1,4,3,5,6,2,9,10,7]
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [6,3,7,5,1,8,9,10,4,2] => [6,7,5,3,8,9,1,10,4,2]
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7] => [8,4,2,1,5,6,3,9,10,7]
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7] => [8,2,3,4,5,6,1,9,10,7]
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [6,3,4,5,7,8,9,10,1,2] => [1,3,4,6,5,7,8,9,10,2]
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [2,1,6,5,7,8,9,10,3,4] => [2,6,5,1,3,7,8,9,10,4]
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [2,5,4,6,7,8,9,1,10,3] => [5,4,2,6,7,8,9,10,1,3]
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [6,8,10,1,7,2,9,3,5,4] => [6,1,8,7,10,2,9,5,3,4]
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,5] => [6,4,2,1,3,7,8,9,10,5]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5] => [6,2,3,4,1,7,8,9,10,5]
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,1,2] => [1,4,3,5,6,7,8,9,10,2]
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3] => [4,2,1,5,6,7,8,9,10,3]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,4,5,6,7,8,9,10,3,12,11] => [12,4,2,1,5,6,7,8,9,10,3,11]
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [10,3,11,5,6,7,8,9,1,12,4,2] => [5,3,6,7,10,11,8,9,12,4,1,2]
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,10,5,6,7,8,9,11,12,3,4] => [2,5,1,3,6,10,7,8,9,11,12,4]
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [4,3,5,6,7,8,9,10,1,2,12,11] => [12,1,4,3,5,6,7,8,9,10,2,11]
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [2,9,4,10,6,7,8,1,11,5,12,3] => [9,4,2,10,6,7,8,11,5,1,12,3]
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,6,7,8,5,10,9,12,11] => [12,10,6,4,2,1,3,7,8,5,9,11]
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [4,3,9,10,6,7,8,12,11,2,5,1] => [4,12,3,2,9,6,7,10,8,11,5,1]
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,4,9,6,7,8,10,11,3,12,5] => [9,6,2,1,4,7,8,10,11,12,3,5]
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [2,3,4,1,6,7,8,5,10,9,12,11] => [12,10,6,2,3,4,1,7,8,5,9,11]
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [10,5,4,6,7,8,9,1,11,12,3,2] => [5,4,6,7,10,8,9,11,12,1,3,2]
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,6,7,8,5,10,11,12,9] => [10,6,4,2,1,3,7,8,5,11,12,9]
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [2,5,4,6,7,8,9,1,10,3,12,11] => [12,5,4,2,6,7,8,9,10,1,3,11]
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [2,3,4,1,6,7,8,5,10,11,12,9] => [10,6,2,3,4,1,7,8,5,11,12,9]
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [2,3,8,5,9,7,1,10,6,11,12,4] => [8,9,7,5,2,3,10,6,1,11,12,4]
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [2,1,8,5,9,7,3,10,6,4,12,11] => [12,8,9,7,5,10,2,1,6,3,4,11]
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [10,3,11,5,1,7,4,9,6,12,8,2] => [10,11,3,9,5,7,12,4,1,6,8,2]
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [2,1,10,5,11,7,3,9,6,12,8,4] => [10,11,5,9,7,12,2,1,6,3,8,4]
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [8,3,9,5,1,7,4,10,6,2,12,11] => [12,8,9,3,7,5,10,4,1,6,2,11]
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [2,5,4,8,9,7,11,10,3,6,12,1] => [5,11,8,4,2,3,9,7,10,6,12,1]
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,1,4,3,8,7,9,10,5,6,12,11] => [12,4,8,7,2,1,3,5,9,10,6,11]
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [4,3,5,8,9,7,12,10,1,11,6,2] => [8,12,9,4,3,5,7,10,11,6,1,2]
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,4,5,8,7,9,10,3,11,12,6] => [8,7,4,2,1,5,9,10,11,3,12,6]
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [2,3,4,1,8,7,9,10,5,6,12,11] => [12,2,8,7,3,4,1,5,9,10,6,11]
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [10,3,4,5,11,7,1,9,6,12,8,2] => [10,11,3,9,4,5,7,12,6,1,8,2]
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [2,1,4,3,10,7,11,9,5,12,8,6] => [10,11,9,7,12,4,2,1,3,8,5,6]
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [8,3,4,5,9,7,1,10,6,2,12,11] => [12,8,9,3,4,7,5,10,6,1,2,11]
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [2,3,4,1,10,7,11,9,5,12,8,6] => [10,11,9,7,12,2,3,4,1,8,5,6]
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [2,9,6,5,7,8,1,10,11,4,12,3] => [6,9,5,2,7,8,10,11,1,4,12,3]
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,6,5,7,8,3,4,10,9,12,11] => [12,10,2,6,5,1,3,7,8,4,9,11]
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [8,3,9,5,1,7,4,10,11,12,6,2] => [8,9,3,7,5,10,4,1,11,12,6,2]
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [2,1,8,5,9,7,3,10,11,12,6,4] => [8,9,7,5,10,2,1,11,3,12,6,4]
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [6,3,7,5,1,8,4,2,10,9,12,11] => [12,10,6,7,5,3,8,4,1,2,9,11]
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [10,3,6,5,7,8,1,9,11,12,4,2] => [6,3,5,10,7,8,9,11,1,12,4,2]
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,6,5,7,8,3,4,10,11,12,9] => [10,2,6,5,1,3,7,8,4,11,12,9]
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [2,3,6,5,7,8,1,9,10,4,12,11] => [12,6,5,2,3,7,8,9,1,10,4,11]
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [6,3,7,5,1,8,4,2,10,11,12,9] => [10,6,7,5,3,8,4,1,2,11,12,9]
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [8,3,4,5,9,7,1,10,11,12,6,2] => [8,9,3,4,7,5,10,11,1,12,6,2]
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,1,4,3,8,7,9,10,11,12,5,6] => [4,8,7,2,1,3,5,9,10,11,12,6]
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [6,3,4,5,7,8,1,2,10,9,12,11] => [12,10,1,3,4,6,5,7,8,2,9,11]
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [2,3,4,1,8,7,9,10,11,12,5,6] => [2,8,7,3,4,1,5,9,10,11,12,6]
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [6,3,4,5,7,8,1,2,10,11,12,9] => [10,1,3,4,6,5,7,8,2,11,12,9]
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [2,3,4,7,6,8,9,1,10,11,12,5] => [7,6,2,3,4,8,9,10,1,11,12,5]
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,4,7,6,8,9,3,10,5,12,11] => [12,7,6,4,2,1,8,9,10,3,5,11]
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [10,3,11,7,6,8,9,4,1,12,5,2] => [7,10,11,3,6,8,9,12,4,5,1,2]
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [2,1,10,7,6,8,9,3,11,12,5,4] => [7,10,6,8,2,9,1,11,12,3,5,4]
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [4,3,7,8,6,10,9,2,5,1,12,11] => [12,4,10,7,3,2,8,6,9,5,1,11]
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [2,9,4,10,6,1,8,5,11,7,12,3] => [9,10,8,2,6,4,11,5,1,7,12,3]
[(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] => [12,10,8,6,4,2,1,3,5,7,9,11]
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [12,3,2,11,6,5,8,7,10,9,4,1] => [4,3,9,10,6,12,8,2,11,7,5,1] => [9,10,12,6,4,3,8,11,7,2,5,1]
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,4,9,6,10,8,3,11,7,12,5] => [9,10,8,6,4,2,1,11,7,3,12,5]
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [2,3,4,1,6,5,8,7,10,9,12,11] => [12,10,8,6,2,3,4,1,5,7,9,11]
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [10,7,4,8,6,1,9,5,11,12,3,2] => [7,8,10,6,4,9,5,11,1,12,3,2]
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,10,11,12,9] => [10,8,6,4,2,1,3,5,7,11,12,9]
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [2,7,4,8,6,1,9,5,10,3,12,11] => [12,7,8,6,4,2,9,5,1,10,3,11]
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [2,3,4,1,6,5,8,7,10,11,12,9] => [10,8,6,2,3,4,1,5,7,11,12,9]
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [2,3,6,5,7,8,9,10,1,11,12,4] => [6,5,2,3,7,8,9,10,11,1,12,4]
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,6,5,7,8,9,10,3,4,12,11] => [12,2,6,5,1,3,7,8,9,10,4,11]
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [10,3,11,5,1,7,8,9,4,12,6,2] => [10,5,3,11,7,1,8,9,12,4,6,2]
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [2,1,10,5,11,7,8,9,3,12,6,4] => [10,11,7,2,1,5,8,9,12,6,3,4]
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [6,3,7,5,1,8,9,10,4,2,12,11] => [12,6,7,5,3,8,9,1,10,4,2,11]
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [2,5,4,6,7,8,9,10,11,1,12,3] => [5,4,2,6,7,8,9,10,11,12,1,3]
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,6,7,8,9,10,5,12,11] => [12,6,4,2,1,3,7,8,9,10,5,11]
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,11,12,1,2] => [1,4,3,5,6,7,8,9,10,11,12,2]
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3] => [4,2,1,5,6,7,8,9,10,11,12,3]
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [2,3,4,1,6,7,8,9,10,5,12,11] => [12,6,2,3,4,1,7,8,9,10,5,11]
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [10,3,4,5,11,7,8,9,1,12,6,2] => [10,3,4,7,5,11,8,9,12,6,1,2]
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,1,4,3,10,7,8,9,11,12,5,6] => [4,10,2,1,7,3,5,8,9,11,12,6]
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [6,3,4,5,7,8,9,10,1,2,12,11] => [12,1,3,4,6,5,7,8,9,10,2,11]
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [2,3,4,1,10,7,8,9,11,12,5,6] => [2,10,3,4,7,1,5,8,9,11,12,6]
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [2,9,4,5,6,10,8,1,11,7,12,3] => [9,10,4,2,8,5,6,11,7,1,12,3]
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,4,5,6,3,8,7,10,9,12,11] => [12,10,8,4,2,1,5,6,3,7,9,11]
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [6,3,9,5,2,10,8,12,11,4,7,1] => [6,12,9,5,10,3,2,8,4,11,7,1]
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [2,1,6,5,9,10,8,12,11,4,7,3] => [6,12,9,5,4,2,1,10,8,11,7,3]
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [4,3,5,6,1,2,8,7,10,9,12,11] => [12,10,8,1,4,3,5,6,2,7,9,11]
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [10,7,4,5,6,8,9,1,11,12,3,2] => [4,5,7,6,10,8,9,11,12,1,3,2]
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,4,5,6,3,8,7,10,11,12,9] => [10,8,4,2,1,5,6,3,7,11,12,9]
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [2,7,4,5,6,8,9,1,10,3,12,11] => [12,4,2,7,5,6,8,9,10,1,3,11]
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [4,3,5,6,1,2,8,7,10,11,12,9] => [10,8,1,4,3,5,6,2,7,11,12,9]
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [6,3,4,5,9,10,8,12,11,2,7,1] => [3,12,9,4,6,5,2,10,8,11,7,1]
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,6,9,8,10,11,5,12,7] => [9,8,6,4,2,1,3,10,11,12,5,7]
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [2,3,4,5,6,1,8,7,10,9,12,11] => [12,10,8,2,3,4,5,6,1,7,9,11]
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [2,3,4,1,6,9,8,10,11,5,12,7] => [9,8,6,2,3,4,1,10,11,12,5,7]
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [2,3,4,5,6,1,8,7,10,11,12,9] => [10,8,2,3,4,5,6,1,7,11,12,9]
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [2,3,8,5,6,7,9,10,1,11,12,4] => [8,2,3,5,6,7,9,10,11,1,12,4]
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,8,5,6,7,9,10,3,4,12,11] => [12,2,8,1,3,5,6,7,9,10,4,11]
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [10,3,11,5,6,7,1,9,4,12,8,2] => [10,5,3,6,11,9,7,12,4,1,8,2]
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [2,1,10,5,6,7,11,9,3,12,8,4] => [10,11,9,5,2,1,6,7,12,8,3,4]
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [8,3,9,5,6,7,1,10,4,2,12,11] => [12,5,3,8,9,6,7,10,4,1,2,11]
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [2,7,4,8,6,1,9,10,11,5,12,3] => [7,8,6,4,2,9,10,1,11,5,12,3]
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,8,9,10,7,12,11] => [12,8,6,4,2,1,3,5,9,10,7,11]
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [4,3,7,8,6,9,10,12,11,5,1,2] => [1,12,7,8,4,3,6,9,10,11,5,2]
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,4,7,6,8,9,10,11,3,12,5] => [7,6,4,2,1,8,9,10,11,12,3,5]
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [2,3,4,1,6,5,8,9,10,7,12,11] => [12,8,6,2,3,4,1,5,9,10,7,11]
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [10,5,4,6,7,1,11,9,3,12,8,2] => [10,11,5,4,9,6,7,12,3,1,8,2]
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,1,4,3,6,5,10,9,11,12,7,8] => [6,10,9,4,2,1,3,5,7,11,12,8]
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [8,5,4,6,7,1,9,10,3,2,12,11] => [12,5,4,8,6,7,9,10,1,3,2,11]
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [2,3,4,1,6,5,10,9,11,12,7,8] => [6,10,9,2,3,4,1,5,7,11,12,8]
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [2,9,4,5,6,7,8,10,11,1,12,3] => [4,2,5,6,9,7,8,10,11,12,1,3]
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,4,5,6,7,8,3,10,9,12,11] => [12,10,4,2,1,5,6,7,8,3,9,11]
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [8,3,9,5,6,7,1,10,11,12,4,2] => [5,3,8,9,6,7,10,11,1,12,4,2]
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,8,5,6,7,9,10,11,12,3,4] => [2,8,1,3,5,6,7,9,10,11,12,4]
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [4,3,5,6,7,8,1,2,10,9,12,11] => [12,10,1,4,3,5,6,7,8,2,9,11]
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [10,3,4,5,6,7,8,9,11,12,1,2] => [1,3,4,5,6,7,8,10,9,11,12,2]
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,4,5,6,7,8,3,10,11,12,9] => [10,4,2,1,5,6,7,8,3,11,12,9]
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11] => [12,2,3,4,5,6,7,8,9,10,1,11]
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [4,3,5,6,7,8,1,2,10,11,12,9] => [10,1,4,3,5,6,7,8,2,11,12,9]
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [8,5,4,6,7,1,9,10,11,12,3,2] => [5,4,8,6,7,9,10,1,11,12,3,2]
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,8,9,10,11,12,7] => [8,6,4,2,1,3,5,9,10,11,12,7]
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [2,5,4,6,7,1,8,3,10,9,12,11] => [12,10,5,4,2,6,7,8,1,3,9,11]
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [2,3,4,1,6,5,8,9,10,11,12,7] => [8,6,2,3,4,1,5,9,10,11,12,7]
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [2,5,4,6,7,1,8,3,10,11,12,9] => [10,5,4,2,6,7,8,1,3,11,12,9]
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [2,7,4,5,6,8,9,10,11,1,12,3] => [4,2,7,5,6,8,9,10,11,12,1,3]
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,4,5,6,3,8,9,10,7,12,11] => [12,8,4,2,1,5,6,3,9,10,7,11]
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [6,3,7,5,1,8,9,10,11,12,4,2] => [6,7,5,3,8,9,1,10,11,12,4,2]
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,6,5,7,8,9,10,11,12,3,4] => [2,6,5,1,3,7,8,9,10,11,12,4]
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [4,3,5,6,1,2,8,9,10,7,12,11] => [12,8,1,4,3,5,6,2,9,10,7,11]
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [10,3,4,5,6,7,11,9,1,12,8,2] => [10,11,3,4,5,6,9,7,12,8,1,2]
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,4,5,6,3,10,9,11,12,7,8] => [4,10,9,2,1,5,6,3,7,11,12,8]
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [8,3,4,5,6,7,9,10,1,2,12,11] => [12,1,3,4,5,6,8,7,9,10,2,11]
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [4,3,5,6,1,2,10,9,11,12,7,8] => [1,10,9,4,3,5,6,2,7,11,12,8]
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [6,3,4,5,7,8,9,10,11,12,1,2] => [1,3,4,6,5,7,8,9,10,11,12,2]
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,11,12,5] => [6,4,2,1,3,7,8,9,10,11,12,5]
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [2,3,4,5,6,1,8,9,10,7,12,11] => [12,8,2,3,4,5,6,1,9,10,7,11]
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,11,12,5] => [6,2,3,4,1,7,8,9,10,11,12,5]
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [2,3,4,5,6,1,10,9,11,12,7,8] => [2,10,9,3,4,5,6,1,7,11,12,8]
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [8,3,4,5,6,7,9,10,11,12,1,2] => [1,3,4,5,6,8,7,9,10,11,12,2]
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,4,5,6,3,8,9,10,11,12,7] => [8,4,2,1,5,6,3,9,10,11,12,7]
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [2,3,4,5,6,7,8,1,10,9,12,11] => [12,10,2,3,4,5,6,7,8,1,9,11]
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [4,3,5,6,1,2,8,9,10,11,12,7] => [8,1,4,3,5,6,2,9,10,11,12,7]
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [2,3,4,5,6,7,8,1,10,11,12,9] => [10,2,3,4,5,6,7,8,1,11,12,9]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [2,3,4,5,6,1,8,9,10,11,12,7] => [8,2,3,4,5,6,1,9,10,11,12,7]
[(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] => [14,12,10,8,6,4,2,1,3,5,7,9,11,13]
[(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] => [16,14,12,10,8,6,4,2,1,3,5,7,9,11,13,15]
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,12,9,11,10] => [12,8,11,6,4,2,1,3,5,7,9,10]
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,10,7,9,8,12,11] => [12,10,6,9,4,2,1,3,5,7,8,11]
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,12,7,8,10,11,9] => [12,6,4,2,10,1,3,5,7,8,11,9]
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,8,5,7,6,10,9,12,11] => [12,10,8,4,7,2,1,3,5,6,9,11]
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,8,5,7,6,12,9,11,10] => [12,8,11,4,7,2,1,3,5,6,9,10]
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,10,5,6,8,9,7,12,11] => [12,10,4,2,1,8,3,5,6,9,7,11]
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,12,5,6,7,9,10,11,8] => [12,4,2,1,3,5,9,6,7,10,11,8]
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,6,3,5,4,8,7,10,9,12,11] => [12,10,8,6,2,5,1,3,4,7,9,11]
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,6,3,5,4,8,7,12,9,11,10] => [12,8,11,6,2,5,1,3,4,7,9,10]
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,3,5,4,10,7,9,8,12,11] => [12,10,6,9,2,5,1,3,4,7,8,11]
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,6,3,5,4,12,7,8,10,11,9] => [12,6,2,5,10,1,3,4,7,8,11,9]
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,8,3,4,6,7,5,10,9,12,11] => [12,10,8,2,1,3,6,4,7,5,9,11]
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,8,3,4,6,7,5,12,9,11,10] => [12,8,11,2,1,3,6,4,7,5,9,10]
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,10,3,4,5,7,8,9,6,12,11] => [12,10,2,1,3,4,5,7,8,9,6,11]
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,12,3,4,5,6,8,9,10,11,7] => [8,2,1,3,4,5,6,12,9,10,11,7]
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [4,1,3,2,6,5,8,7,10,9,12,11] => [12,10,8,6,4,1,3,2,5,7,9,11]
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [4,1,3,2,6,5,8,7,12,9,11,10] => [12,8,11,6,4,1,3,2,5,7,9,10]
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [4,1,3,2,6,5,10,7,9,8,12,11] => [12,10,6,9,4,1,3,2,5,7,8,11]
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [4,1,3,2,6,5,12,7,8,10,11,9] => [12,6,4,1,10,3,2,5,7,8,11,9]
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [4,1,3,2,8,5,7,6,10,9,12,11] => [12,10,8,4,7,1,3,2,5,6,9,11]
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [4,1,3,2,8,5,7,6,12,9,11,10] => [12,8,11,4,7,1,3,2,5,6,9,10]
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [4,1,3,2,10,5,6,8,9,7,12,11] => [12,10,4,1,3,8,2,5,6,9,7,11]
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [4,1,3,2,12,5,6,7,9,10,11,8] => [12,4,1,3,2,5,9,6,7,10,11,8]
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [6,1,2,4,5,3,8,7,10,9,12,11] => [12,10,8,4,1,2,6,5,3,7,9,11]
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [6,1,2,4,5,3,8,7,12,9,11,10] => [12,8,11,4,1,2,6,5,3,7,9,10]
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [6,1,2,4,5,3,10,7,9,8,12,11] => [12,10,4,9,1,2,6,5,3,7,8,11]
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [6,1,2,4,5,3,12,7,8,10,11,9] => [12,4,1,2,10,6,5,3,7,8,11,9]
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [8,1,2,3,5,6,7,4,10,9,12,11] => [12,10,5,1,2,3,6,8,7,4,9,11]
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [8,1,2,3,5,6,7,4,12,9,11,10] => [12,5,11,1,2,3,6,8,7,4,9,10]
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [10,1,2,3,4,6,7,8,9,5,12,11] => [12,6,1,2,3,4,7,8,10,9,5,11]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,1,2,3,4,5,7,8,9,10,11,6] => [7,1,2,3,4,5,8,9,10,12,11,6]
[(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] => [18,16,14,12,10,8,6,4,2,1,3,5,7,9,11,13,15,17]
[(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] => [20,18,16,14,12,10,8,6,4,2,1,3,5,7,9,11,13,15,17,19]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).