Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Images
[(1,2)] => [2,1] => [2,1] => [2,1]
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3]
[(1,3),(2,4)] => [3,4,1,2] => [4,3,2,1] => [2,3,4,1]
[(1,4),(2,3)] => [4,3,2,1] => [4,3,2,1] => [2,3,4,1]
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5]
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,3,2,1,6,5] => [2,3,4,1,6,5]
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [2,3,4,1,6,5]
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [6,5,3,4,2,1] => [2,4,5,3,6,1]
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [2,4,5,3,6,1]
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [2,3,4,5,6,1]
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [6,5,4,3,2,1] => [2,3,4,5,6,1]
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => [2,3,4,5,6,1]
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [5,6,3,4,1,2] => [4,1,6,3,5,2]
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => [2,1,4,5,6,3]
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,4,5,6,3]
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [6,5,3,4,2,1] => [2,4,5,3,6,1]
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => [2,3,4,5,6,1]
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [2,3,4,5,6,1]
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [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] => [2,1,4,3,6,5,8,7]
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7]
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7]
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [6,5,3,4,2,1,8,7] => [2,4,5,3,6,1,8,7]
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [6,5,3,4,2,1,8,7] => [2,4,5,3,6,1,8,7]
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [8,7,3,5,4,6,2,1] => [2,6,5,7,3,4,8,1]
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [8,7,3,5,4,6,2,1] => [2,6,5,7,3,4,8,1]
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [8,7,5,4,3,6,2,1] => [2,6,4,5,7,3,8,1]
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [8,7,5,4,3,6,2,1] => [2,6,4,5,7,3,8,1]
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7]
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7]
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7]
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [5,6,3,4,1,2,8,7] => [4,1,6,3,5,2,8,7]
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7]
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7]
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [6,5,3,4,2,1,8,7] => [2,4,5,3,6,1,8,7]
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7]
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7]
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7]
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [8,7,5,4,3,6,2,1] => [2,6,4,5,7,3,8,1]
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [8,7,5,4,3,6,2,1] => [2,6,4,5,7,3,8,1]
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1]
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1]
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [7,8,5,4,3,6,1,2] => [6,1,4,5,8,3,7,2]
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [7,8,5,4,3,6,1,2] => [6,1,4,5,8,3,7,2]
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [7,8,3,5,4,6,1,2] => [6,1,5,8,3,4,7,2]
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,8,7,5,6,4,3] => [2,1,4,6,7,5,8,3]
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,8,7,5,6,4,3] => [2,1,4,6,7,5,8,3]
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [8,7,3,5,4,6,2,1] => [2,6,5,7,3,4,8,1]
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [8,7,5,4,3,6,2,1] => [2,6,4,5,7,3,8,1]
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [8,7,5,4,3,6,2,1] => [2,6,4,5,7,3,8,1]
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1]
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [8,7,3,6,5,4,2,1] => [2,4,5,6,7,3,8,1]
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3]
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3]
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [7,8,3,6,5,4,1,2] => [4,1,5,6,8,3,7,2]
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [7,8,6,4,5,3,1,2] => [3,1,5,6,4,8,7,2]
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [7,8,6,4,5,3,1,2] => [3,1,5,6,4,8,7,2]
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [6,8,3,7,5,1,4,2] => [4,5,7,3,8,6,1,2]
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3]
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,6,3,4] => [2,1,6,3,8,5,7,4]
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,6,2,4] => [6,8,7,3,5,1,2,4]
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [7,5,8,4,2,6,1,3] => [6,4,2,8,7,5,1,3]
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [7,5,8,4,2,6,1,3] => [6,4,2,8,7,5,1,3]
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1]
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1]
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [8,7,3,6,5,4,2,1] => [2,4,5,6,7,3,8,1]
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [8,7,3,6,5,4,2,1] => [2,4,5,6,7,3,8,1]
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [8,6,3,7,5,2,4,1] => [4,5,7,3,6,8,2,1]
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [7,5,3,8,2,6,1,4] => [6,8,5,3,7,2,1,4]
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5]
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5]
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5]
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5]
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5]
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5]
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [8,5,3,7,2,6,4,1] => [4,6,7,5,8,3,2,1]
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [8,6,3,7,5,2,4,1] => [4,5,7,3,6,8,2,1]
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [8,7,3,6,5,4,2,1] => [2,4,5,6,7,3,8,1]
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [8,7,3,6,5,4,2,1] => [2,4,5,6,7,3,8,1]
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [8,5,7,4,2,6,3,1] => [3,6,4,7,8,5,2,1]
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [8,5,7,4,2,6,3,1] => [3,6,4,7,8,5,2,1]
>>> Load all 262 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [5,8,3,7,1,6,4,2] => [4,6,7,8,5,3,1,2]
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,8,7,5,6,4,3] => [2,1,4,6,7,5,8,3]
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3]
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [6,8,3,7,5,1,4,2] => [4,5,7,3,8,6,1,2]
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1]
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1]
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [7,8,3,6,5,4,1,2] => [4,1,5,6,8,3,7,2]
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3]
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3]
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [8,7,3,6,5,4,2,1] => [2,4,5,6,7,3,8,1]
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1]
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1]
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [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] => [2,1,4,3,6,5,8,7,10,9]
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9]
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9]
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => [2,3,4,5,6,1,8,7,10,9]
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => [2,1,4,5,6,3,8,7,10,9]
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => [2,1,4,5,6,3,8,7,10,9]
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => [2,3,4,5,6,1,8,7,10,9]
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9]
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [10,9,7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,9,3,10,1]
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => [10,9,8,6,5,4,7,3,2,1] => [2,3,7,5,6,8,4,9,10,1]
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9]
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9]
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9]
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,6,7,8,5,10,9]
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,6,7,8,5,10,9]
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9]
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9]
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9]
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [10,9,7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,9,3,10,1]
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [10,9,7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,9,3,10,1]
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [10,9,3,8,7,6,5,4,2,1] => [2,4,5,6,7,8,9,3,10,1]
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3]
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,4),(2,9),(3,10),(5,7),(6,8)] => [4,9,10,1,7,8,5,6,2,3] => [10,9,8,4,7,6,5,3,2,1] => [2,3,5,6,7,8,4,9,10,1]
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3]
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5]
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,5]
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7]
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7]
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7]
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,8,9,10,7]
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,8,9,10,7]
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7]
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7]
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7]
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,7),(2,10),(3,5),(4,9),(6,8)] => [7,10,5,9,3,8,1,6,4,2] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,5]
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5]
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [10,9,3,8,7,6,5,4,2,1] => [2,4,5,6,7,8,9,3,10,1]
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3]
[(1,3),(2,10),(4,9),(5,8),(6,7)] => [3,10,1,9,8,7,6,5,4,2] => [10,9,3,8,7,6,5,4,2,1] => [2,4,5,6,7,8,9,3,10,1]
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [9,10,8,7,6,5,4,3,1,2] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1]
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [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] => [12,11,10,9,8,7,6,5,4,3,2,1] => [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] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,4,5,6,7,8,9,10,3,12,11]
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,6,7,8,5,10,9,12,11]
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3]
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => [2,3,4,1,6,7,8,5,10,9,12,11]
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,6,7,8,5,10,11,12,9]
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11]
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [4,3,2,1,8,7,6,5,12,11,10,9] => [2,3,4,1,6,7,8,5,10,11,12,9]
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3]
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11]
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,4,5,6,7,8,9,10,3,12,11]
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [12,11,10,9,6,5,8,7,4,3,2,1] => [2,3,4,7,6,8,9,5,10,11,12,1]
[(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] => [2,1,4,3,6,5,8,7,10,9,12,11]
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3]
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => [2,3,4,1,6,5,8,7,10,9,12,11]
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,10,11,12,9]
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11]
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [4,3,2,1,6,5,8,7,12,11,10,9] => [2,3,4,1,6,5,8,7,10,11,12,9]
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,6,7,8,9,10,5,12,11]
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3]
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [4,3,2,1,10,9,8,7,6,5,12,11] => [2,3,4,1,6,7,8,9,10,5,12,11]
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [12,11,10,9,6,5,8,7,4,3,2,1] => [2,3,4,7,6,8,9,5,10,11,12,1]
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,4,5,6,3,8,7,10,9,12,11]
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,4,5,6,3,8,7,10,11,12,9]
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11]
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,11,12,5]
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [6,5,4,3,2,1,8,7,10,9,12,11] => [2,3,4,5,6,1,8,7,10,9,12,11]
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [4,3,2,1,12,11,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,11,12,5]
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [6,5,4,3,2,1,8,7,12,11,10,9] => [2,3,4,5,6,1,8,7,10,11,12,9]
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [12,11,10,9,6,5,8,7,4,3,2,1] => [2,3,4,7,6,8,9,5,10,11,12,1]
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,8,9,10,7,12,11]
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3]
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => [2,3,4,1,6,5,8,9,10,7,12,11]
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,4,5,6,7,8,3,10,9,12,11]
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,4,5,6,7,8,3,10,11,12,9]
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11]
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,8,9,10,11,12,7]
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [8,7,6,5,4,3,2,1,10,9,12,11] => [2,3,4,5,6,7,8,1,10,9,12,11]
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [4,3,2,1,6,5,12,11,10,9,8,7] => [2,3,4,1,6,5,8,9,10,11,12,7]
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [8,7,6,5,4,3,2,1,12,11,10,9] => [2,3,4,5,6,7,8,1,10,11,12,9]
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [12,11,10,9,6,5,8,7,4,3,2,1] => [2,3,4,7,6,8,9,5,10,11,12,1]
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,4,5,6,3,8,9,10,7,12,11]
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,11,12,5]
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [6,5,4,3,2,1,10,9,8,7,12,11] => [2,3,4,5,6,1,8,9,10,7,12,11]
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [4,3,2,1,12,11,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,11,12,5]
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,4,5,6,3,8,9,10,11,12,7]
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [8,7,6,5,4,3,2,1,10,9,12,11] => [2,3,4,5,6,7,8,1,10,9,12,11]
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [8,7,6,5,4,3,2,1,12,11,10,9] => [2,3,4,5,6,7,8,1,10,11,12,9]
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [6,5,4,3,2,1,12,11,10,9,8,7] => [2,3,4,5,6,1,8,9,10,11,12,7]
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,10,11,12,9]
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,8,9,10,7,12,11]
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,8,9,10,11,12,7]
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,6,7,8,5,10,9,12,11]
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,6,7,8,5,10,11,12,9]
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,6,7,8,9,10,5,12,11]
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,11,12,5]
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,4,5,6,3,8,7,10,9,12,11]
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,4,5,6,3,8,7,10,11,12,9]
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,4,5,6,3,8,9,10,7,12,11]
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,4,5,6,3,8,9,10,11,12,7]
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,4,5,6,7,8,3,10,9,12,11]
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,4,5,6,7,8,3,10,11,12,9]
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,4,5,6,7,8,9,10,3,12,11]
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3]
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => [2,3,4,1,6,5,8,7,10,9,12,11]
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [4,3,2,1,6,5,8,7,12,11,10,9] => [2,3,4,1,6,5,8,7,10,11,12,9]
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => [2,3,4,1,6,5,8,9,10,7,12,11]
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [4,3,2,1,6,5,12,11,10,9,8,7] => [2,3,4,1,6,5,8,9,10,11,12,7]
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => [2,3,4,1,6,7,8,5,10,9,12,11]
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [4,3,2,1,8,7,6,5,12,11,10,9] => [2,3,4,1,6,7,8,5,10,11,12,9]
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [4,3,2,1,10,9,8,7,6,5,12,11] => [2,3,4,1,6,7,8,9,10,5,12,11]
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [4,3,2,1,12,11,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,11,12,5]
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [6,5,4,3,2,1,8,7,10,9,12,11] => [2,3,4,5,6,1,8,7,10,9,12,11]
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [6,5,4,3,2,1,8,7,12,11,10,9] => [2,3,4,5,6,1,8,7,10,11,12,9]
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [6,5,4,3,2,1,10,9,8,7,12,11] => [2,3,4,5,6,1,8,9,10,7,12,11]
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [6,5,4,3,2,1,12,11,10,9,8,7] => [2,3,4,5,6,1,8,9,10,11,12,7]
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [8,7,6,5,4,3,2,1,10,9,12,11] => [2,3,4,5,6,7,8,1,10,9,12,11]
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [8,7,6,5,4,3,2,1,12,11,10,9] => [2,3,4,5,6,7,8,1,10,11,12,9]
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
  • $des$ is the number of descents, St000021The number of descents of a permutation.,
  • $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
  • $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
  • $Ebot$ is the sum of the excedance bottoms,
  • $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
  • $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
  • $Res$ is the sum of the (right) embracing numbers,
  • $Ine$ is the sum of the side numbers.