- FindStat

Identifier

Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions

Images

[(1,2)] => [2,1] => [2,1] => {{1,2}}

[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => {{1,2},{3,4}}

[(1,3),(2,4)] => [3,4,1,2] => [2,4,3,1] => {{1,2,4},{3}}

[(1,4),(2,3)] => [4,3,2,1] => [4,1,2,3] => {{1,2,3,4}}

[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}

[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [2,4,3,1,6,5] => {{1,2,4},{3},{5,6}}

[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}}

[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [4,5,2,6,3,1] => {{1,4,6},{2,3,5}}

[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [6,5,2,1,4,3] => {{1,2,3,4,5,6}}

[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [6,3,1,5,2,4] => {{1,2,3,4,5,6}}

[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [3,1,6,5,4,2] => {{1,2,3,6},{4,5}}

[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [2,3,6,4,5,1] => {{1,2,3,6},{4},{5}}

[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [5,4,3,6,1,2] => {{1,5},{2,4,6},{3}}

[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,4,6,5,3] => {{1,2},{3,4,6},{5}}

[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}}

[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [5,6,3,2,4,1] => {{1,2,4,5,6},{3}}

[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [3,6,2,4,1,5] => {{1,2,3,5,6},{4}}

[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [2,6,1,3,5,4] => {{1,2,3,4,6},{5}}

[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}}

[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}

[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [2,4,3,1,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}}

[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}

[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [4,5,2,6,3,1,8,7] => {{1,4,6},{2,3,5},{7,8}}

[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [6,5,2,1,4,3,8,7] => {{1,2,3,4,5,6},{7,8}}

[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [6,5,2,7,4,8,3,1] => {{1,6,8},{2,3,4,5,7}}

[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [8,5,2,7,4,1,6,3] => {{1,2,3,4,5,6,7,8}}

[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [8,3,7,5,2,1,6,4] => {{1,2,3,4,5,6,7,8}}

[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [6,3,7,5,2,8,4,1] => {{1,6,8},{2,3,4,5,7}}

[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [6,3,1,5,2,4,8,7] => {{1,2,3,4,5,6},{7,8}}

[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [3,1,6,5,4,2,8,7] => {{1,2,3,6},{4,5},{7,8}}

[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [2,3,6,4,5,1,8,7] => {{1,2,3,6},{4},{5},{7,8}}

[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [5,4,3,6,1,2,8,7] => {{1,5},{2,4,6},{3},{7,8}}

[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,4,6,5,3,8,7] => {{1,2},{3,4,6},{5},{7,8}}

[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,6,3,4,5,8,7] => {{1,2},{3,4,5,6},{7,8}}

[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [5,6,3,2,4,1,8,7] => {{1,2,4,5,6},{3},{7,8}}

[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [3,6,2,4,1,5,8,7] => {{1,2,3,5,6},{4},{7,8}}

[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [2,6,1,3,5,4,8,7] => {{1,2,3,4,6},{5},{7,8}}

[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [6,1,2,3,4,5,8,7] => {{1,2,3,4,5,6},{7,8}}

[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [6,7,2,3,4,8,5,1] => {{1,6,8},{2,3,4,5,7}}

[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [8,7,2,3,4,1,6,5] => {{1,2,3,4,5,6,7,8}}

[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [8,5,7,3,1,4,2,6] => {{1,2,3,4,5,6,7,8}}

[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [5,1,7,3,8,4,6,2] => {{1,2,5,8},{3,4,6,7}}

[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [2,5,7,3,8,6,4,1] => {{1,2,5,8},{3,4,7},{6}}

[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [7,6,1,3,5,8,4,2] => {{1,3,4,7},{2,6,8},{5}}

[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [3,6,7,4,1,8,5,2] => {{1,3,5,7},{2,6,8},{4}}

[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [5,6,3,7,4,8,1,2] => {{1,4,5,7},{2,6,8},{3}}

[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,6,7,4,8,5,3] => {{1,2},{3,6,8},{4,5,7}}

[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,8,7,4,3,6,5] => {{1,2},{3,4,5,6,7,8}}

[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [5,8,3,7,4,2,6,1] => {{1,2,4,5,6,7,8},{3}}

[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [3,8,7,4,1,2,6,5] => {{1,2,3,5,6,7,8},{4}}

[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [7,8,1,3,5,2,6,4] => {{1,2,3,4,6,7,8},{5}}

[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [5,8,7,3,2,6,1,4] => {{1,2,3,4,5,7,8},{6}}

[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [2,8,6,3,1,5,7,4] => {{1,2,3,4,5,6,8},{7}}

[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [8,1,6,3,2,5,4,7] => {{1,2,3,4,5,6,7,8}}

[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [8,1,4,2,6,3,5,7] => {{1,2,3,4,5,6,7,8}}

[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [2,8,4,1,6,3,7,5] => {{1,2,3,4,5,6,8},{7}}

[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [4,8,1,2,7,6,3,5] => {{1,2,3,4,5,7,8},{6}}

[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [3,8,4,2,5,7,1,6] => {{1,2,3,4,6,7,8},{5}}

[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [7,8,5,4,2,1,3,6] => {{1,2,3,5,6,7,8},{4}}

[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [6,8,3,5,2,7,4,1] => {{1,2,4,5,6,7,8},{3}}

[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,8,5,3,7,4,6] => {{1,2},{3,4,5,6,7,8}}

[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,5,3,8,7,6,4] => {{1,2},{3,4,5,8},{6,7}}

[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [6,5,3,2,8,7,1,4] => {{1,6,7},{2,4,5,8},{3}}

[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [7,5,2,4,8,1,6,3] => {{1,6,7},{2,3,5,8},{4}}

[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [3,4,2,8,5,7,6,1] => {{1,2,3,4,8},{5},{6,7}}

[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [2,4,1,8,7,6,5,3] => {{1,2,3,4,8},{5,7},{6}}

[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [4,1,2,8,7,5,6,3] => {{1,2,3,4,8},{5,6,7}}

[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [8,4,2,1,7,5,3,6] => {{1,2,3,4,5,6,7,8}}

[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [8,3,4,1,6,7,2,5] => {{1,2,3,4,5,6,7,8}}

[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [4,3,1,8,6,7,5,2] => {{1,2,3,4,8},{5,6,7}}

[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [3,1,4,8,6,5,7,2] => {{1,2,3,4,8},{5,6},{7}}

[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [2,3,4,8,5,6,7,1] => {{1,2,3,4,8},{5},{6},{7}}

[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [7,3,5,4,8,6,1,2] => {{1,7},{2,3,5,8},{4},{6}}

[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [6,4,3,5,8,1,7,2] => {{1,6},{2,4,5,8},{3},{7}}

[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,4,5,8,6,7,3] => {{1,2},{3,4,5,8},{6},{7}}

[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,7,6,5,8,3,4] => {{1,2},{3,7},{4,6,8},{5}}

[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [5,7,3,6,1,8,2,4] => {{1,5},{2,7},{3},{4,6,8}}

[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [2,7,6,4,5,8,1,3] => {{1,2,7},{3,6,8},{4},{5}}

[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [7,1,6,5,4,8,2,3] => {{1,2,7},{3,6,8},{4,5}}

[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [3,7,5,6,8,4,2,1] => {{1,3,5,8},{2,7},{4,6}}

[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [5,7,1,6,8,2,4,3] => {{1,3,5,8},{2,4,6,7}}

[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [8,7,5,6,1,2,3,4] => {{1,2,3,4,5,6,7,8}}

[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [8,6,2,5,1,7,4,3] => {{1,2,3,4,5,6,7,8}}

[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [5,6,2,1,8,7,3,4] => {{1,4,5,8},{2,3,6,7}}

[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [4,6,2,5,8,3,7,1] => {{1,4,5,8},{2,3,6},{7}}

[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [7,5,2,6,3,8,1,4] => {{1,7},{2,3,5},{4,6,8}}

[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [4,1,2,3,6,8,7,5] => {{1,2,3,4},{5,6,8},{7}}

[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [2,4,3,1,6,8,7,5] => {{1,2,4},{3},{5,6,8},{7}}

[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,6,8,7,5] => {{1,2},{3,4},{5,6,8},{7}}

[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,5,6,7] => {{1,2},{3,4},{5,6,7,8}}

[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [2,4,3,1,8,5,6,7] => {{1,2,4},{3},{5,6,7,8}}

[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [4,1,2,3,8,5,6,7] => {{1,2,3,4},{5,6,7,8}}

[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [7,5,2,8,3,4,6,1] => {{1,4,6,7,8},{2,3,5}}

[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [5,6,2,8,4,3,1,7] => {{1,4,5,7,8},{2,3,6}}

[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [4,7,2,8,1,5,3,6] => {{1,4,5,6,8},{2,3,7}}

[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [8,7,2,1,4,5,6,3] => {{1,2,3,4,5,6,7,8}}

[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [8,6,1,7,3,5,2,4] => {{1,2,3,4,5,6,7,8}}

[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [3,6,8,7,1,5,4,2] => {{1,2,3,5,6,8},{4,7}}

[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [5,7,8,6,3,4,1,2] => {{1,2,3,5,7,8},{4,6}}

[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [7,1,8,5,4,3,6,2] => {{1,2,3,6,7,8},{4,5}}

[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [2,7,8,4,5,3,6,1] => {{1,2,3,6,7,8},{4},{5}}

>>> Load all 350 entries. <<<

[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [5,7,3,8,1,4,6,2] => {{1,5},{2,4,6,7,8},{3}}

[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,7,8,5,4,6,3] => {{1,2},{3,4,6,7,8},{5}}

[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,5,8,4,6,3,7] => {{1,2},{3,4,5,7,8},{6}}

[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [6,5,3,8,4,1,2,7] => {{1,6},{2,4,5,7,8},{3}}

[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [7,5,8,4,3,6,2,1] => {{1,2,3,5,7,8},{4},{6}}

[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [2,4,8,3,5,6,1,7] => {{1,2,3,4,7,8},{5},{6}}

[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [4,1,8,3,6,5,2,7] => {{1,2,3,4,7,8},{5,6}}

[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [3,4,8,1,7,2,5,6] => {{1,2,3,4,6,8},{5,7}}

[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [8,4,1,3,7,2,6,5] => {{1,2,3,4,5,6,7,8}}

[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [8,3,1,2,4,7,5,6] => {{1,2,3,4,5,6,7,8}}

[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [3,1,8,2,4,7,6,5] => {{1,2,3,4,5,8},{6,7}}

[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [2,3,8,1,4,6,7,5] => {{1,2,3,4,5,8},{6},{7}}

[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [4,3,8,2,5,1,7,6] => {{1,2,3,4,6,8},{5},{7}}

[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [6,3,8,4,2,5,7,1] => {{1,2,3,5,6,8},{4},{7}}

[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [7,4,3,8,2,5,1,6] => {{1,7},{2,4,5,6,8},{3}}

[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,4,8,3,5,7,6] => {{1,2},{3,4,5,6,8},{7}}

[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,8,3,4,5,6,7] => {{1,2},{3,4,5,6,7,8}}

[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [7,8,3,2,4,5,6,1] => {{1,2,4,5,6,7,8},{3}}

[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [6,8,2,4,3,5,1,7] => {{1,2,3,5,6,7,8},{4}}

[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [4,8,2,3,5,1,6,7] => {{1,2,3,4,6,7,8},{5}}

[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [3,8,2,1,4,6,5,7] => {{1,2,3,4,5,7,8},{6}}

[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [2,8,1,3,4,5,7,6] => {{1,2,3,4,5,6,8},{7}}

[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [8,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}}

[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}

[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [2,4,3,1,6,5,8,7,10,9] => {{1,2,4},{3},{5,6},{7,8},{9,10}}

[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [4,1,2,3,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}

[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [6,5,2,1,4,3,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}}

[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [8,5,2,7,4,1,6,3,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}

[(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [10,5,2,7,4,9,6,1,8,3] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [2,3,6,4,5,1,8,7,10,9] => {{1,2,3,6},{4},{5},{7,8},{9,10}}

[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,4,6,5,3,8,7,10,9] => {{1,2},{3,4,6},{5},{7,8},{9,10}}

[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,6,3,4,5,8,7,10,9] => {{1,2},{3,4,5,6},{7,8},{9,10}}

[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [6,1,2,3,4,5,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}}

[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [8,7,2,3,4,1,6,5,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}

[(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [10,7,2,3,4,9,6,1,8,5] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [2,1,8,7,4,3,6,5,10,9] => {{1,2},{3,4,5,6,7,8},{9,10}}

[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [8,1,6,3,2,5,4,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}

[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [10,9,6,3,2,5,4,1,8,7] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [2,1,10,7,4,9,6,3,8,5] => {{1,2},{3,4,5,6,7,8,9,10}}

[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [10,1,6,3,8,5,2,7,4,9] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => [2,7,4,9,6,3,10,8,5,1] => {{1,2,7,10},{3,4,5,6,9},{8}}

[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [2,3,4,8,5,6,7,1,10,9] => {{1,2,3,4,8},{5},{6},{7},{9,10}}

[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,4,5,8,6,7,3,10,9] => {{1,2},{3,4,5,8},{6},{7},{9,10}}

[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [2,4,3,1,6,8,7,5,10,9] => {{1,2,4},{3},{5,6,8},{7},{9,10}}

[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,6,8,7,5,10,9] => {{1,2},{3,4},{5,6,8},{7},{9,10}}

[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,8,5,6,7,10,9] => {{1,2},{3,4},{5,6,7,8},{9,10}}

[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [4,1,2,3,8,5,6,7,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}

[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [8,7,2,1,4,5,6,3,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}

[(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [10,7,2,9,4,5,6,1,8,3] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,8,3,4,5,6,7,10,9] => {{1,2},{3,4,5,6,7,8},{9,10}}

[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [8,1,2,3,4,5,6,7,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}

[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [8,9,2,3,4,5,6,10,7,1] => {{1,8,10},{2,3,4,5,6,7,9}}

[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [10,9,2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [2,1,10,9,4,5,6,3,8,7] => {{1,2},{3,4,5,6,7,8,9,10}}

[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [10,1,8,3,4,5,2,7,6,9] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [2,1,4,3,10,9,6,5,8,7] => {{1,2},{3,4},{5,6,7,8,9,10}}

[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [4,1,2,3,10,9,6,5,8,7] => {{1,2,3,4},{5,6,7,8,9,10}}

[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [10,9,2,1,8,5,4,7,6,3] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,10,3,8,5,4,7,6,9] => {{1,2},{3,4,5,6,7,8,9,10}}

[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [10,1,2,7,4,3,6,5,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [10,3,1,5,2,7,4,9,6,8] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,4,5,6,10,7,8,9,3] => {{1,2},{3,4,5,6,10},{7},{8},{9}}

[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [2,3,4,5,10,6,7,8,9,1] => {{1,2,3,4,5,10},{6},{7},{8},{9}}

[(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => [4,7,2,5,6,10,3,8,9,1] => {{1,4,5,6,10},{2,3,7},{8},{9}}

[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [2,4,3,1,6,7,10,8,9,5] => {{1,2,4},{3},{5,6,7,10},{8},{9}}

[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,6,7,10,8,9,5] => {{1,2},{3,4},{5,6,7,10},{8},{9}}

[(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => [6,8,2,3,4,7,10,5,9,1] => {{1,6,7,10},{2,3,4,5,8},{9}}

[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,4,6,5,3,8,10,9,7] => {{1,2},{3,4,6},{5},{7,8,10},{9}}

[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [2,3,6,4,5,1,8,10,9,7] => {{1,2,3,6},{4},{5},{7,8,10},{9}}

[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [2,4,3,1,6,5,8,10,9,7] => {{1,2,4},{3},{5,6},{7,8,10},{9}}

[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,8,10,9,7] => {{1,2},{3,4},{5,6},{7,8,10},{9}}

[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,10,7,8,9] => {{1,2},{3,4},{5,6},{7,8,9,10}}

[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [4,1,2,3,6,5,10,7,8,9] => {{1,2,3,4},{5,6},{7,8,9,10}}

[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [6,5,2,1,4,3,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}

[(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [10,5,2,9,4,1,6,7,8,3] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,6,3,4,5,10,7,8,9] => {{1,2},{3,4,5,6},{7,8,9,10}}

[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [6,1,2,3,4,5,10,7,8,9] => {{1,2,3,4,5,6},{7,8,9,10}}

[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [10,9,2,3,4,1,6,7,8,5] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [2,1,10,9,4,3,6,7,8,5] => {{1,2},{3,4,5,6,7,8,9,10}}

[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [10,1,8,3,2,5,6,7,4,9] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [4,6,8,10,9,1,5,2,7,3] => {{1,2,3,4,6,8,10},{5,7,9}}

[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,10,5,6,7,8,9] => {{1,2},{3,4},{5,6,7,8,9,10}}

[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [4,1,2,3,10,5,6,7,8,9] => {{1,2,3,4},{5,6,7,8,9,10}}

[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [10,9,2,1,4,5,6,7,8,3] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,3,4,5,6,7,8,9] => {{1,2},{3,4,5,6,7,8,9,10}}

[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [10,1,2,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [12,1,2,3,4,5,6,7,8,9,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,10,3,4,5,6,7,8,9,12,11] => {{1,2},{3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [12,9,2,11,4,5,6,7,8,1,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,12,11,4,5,6,7,8,3,10,9] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [10,9,2,1,4,5,6,7,8,3,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [12,1,8,3,10,5,6,7,2,9,4,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,8,5,6,7,10,9,12,11] => {{1,2},{3,4},{5,6,7,8},{9,10},{11,12}}

[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [12,11,2,1,10,5,6,7,4,9,8,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,12,3,10,5,6,7,4,9,8,11] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [4,1,2,3,8,5,6,7,10,9,12,11] => {{1,2,3,4},{5,6,7,8},{9,10},{11,12}}

[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [12,11,8,3,2,5,6,7,4,1,10,9] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,8,5,6,7,12,9,10,11] => {{1,2},{3,4},{5,6,7,8},{9,10,11,12}}

[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [10,1,8,3,2,5,6,7,4,9,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [4,1,2,3,8,5,6,7,12,9,10,11] => {{1,2,3,4},{5,6,7,8},{9,10,11,12}}

[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [12,1,2,7,4,9,6,3,8,5,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [2,1,10,7,4,9,6,3,8,5,12,11] => {{1,2},{3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [12,5,2,7,4,9,6,11,8,1,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [2,1,12,7,4,9,6,11,8,3,10,5] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [10,5,2,7,4,9,6,1,8,3,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [12,1,10,3,2,9,6,5,8,7,4,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,1,4,3,10,9,6,5,8,7,12,11] => {{1,2},{3,4},{5,6,7,8,9,10},{11,12}}

[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [12,11,2,1,4,9,6,5,8,7,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,12,3,4,9,6,5,8,7,10,11] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [4,1,2,3,10,9,6,5,8,7,12,11] => {{1,2,3,4},{5,6,7,8,9,10},{11,12}}

[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [12,7,2,3,4,9,6,11,8,1,10,5] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [2,1,4,3,12,9,6,11,8,5,10,7] => {{1,2},{3,4},{5,6,7,8,9,10,11,12}}

[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [10,7,2,3,4,9,6,1,8,5,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [4,1,2,3,12,9,6,11,8,5,10,7] => {{1,2,3,4},{5,6,7,8,9,10,11,12}}

[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [12,1,10,7,4,3,6,5,2,9,8,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,8,7,4,3,6,5,10,9,12,11] => {{1,2},{3,4,5,6,7,8},{9,10},{11,12}}

[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [12,5,2,7,4,11,6,1,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [2,1,12,7,4,11,6,3,8,9,10,5] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [8,5,2,7,4,1,6,3,10,9,12,11] => {{1,2,3,4,5,6,7,8},{9,10},{11,12}}

[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [12,11,2,7,4,3,6,5,8,1,10,9] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,8,7,4,3,6,5,12,9,10,11] => {{1,2},{3,4,5,6,7,8},{9,10,11,12}}

[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [10,1,2,7,4,3,6,5,8,9,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [8,5,2,7,4,1,6,3,12,9,10,11] => {{1,2,3,4,5,6,7,8},{9,10,11,12}}

[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [12,7,2,3,4,11,6,1,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,1,4,3,12,11,6,5,8,9,10,7] => {{1,2},{3,4},{5,6,7,8,9,10,11,12}}

[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [8,7,2,3,4,1,6,5,10,9,12,11] => {{1,2,3,4,5,6,7,8},{9,10},{11,12}}

[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [4,1,2,3,12,11,6,5,8,9,10,7] => {{1,2,3,4},{5,6,7,8,9,10,11,12}}

[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [8,7,2,3,4,1,6,5,12,9,10,11] => {{1,2,3,4,5,6,7,8},{9,10,11,12}}

[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [12,1,2,3,8,5,4,7,6,9,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,10,3,8,5,4,7,6,9,12,11] => {{1,2},{3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [12,9,2,11,8,5,4,7,6,1,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [2,1,12,11,8,5,4,7,6,3,10,9] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [10,9,2,1,8,5,4,7,6,3,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [12,1,6,3,8,5,10,7,2,9,4,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}

[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [12,3,2,11,6,5,8,7,10,9,4,1] => [12,11,2,1,8,5,10,7,4,9,6,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,12,3,8,5,10,7,4,9,6,11] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [4,1,2,3,6,5,8,7,10,9,12,11] => {{1,2,3,4},{5,6},{7,8},{9,10},{11,12}}

[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [12,11,6,3,8,5,2,7,4,1,10,9] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,12,9,10,11] => {{1,2},{3,4},{5,6},{7,8},{9,10,11,12}}

[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [10,1,6,3,8,5,2,7,4,9,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [4,1,2,3,6,5,8,7,12,9,10,11] => {{1,2,3,4},{5,6},{7,8},{9,10,11,12}}

[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [12,1,2,9,4,3,6,7,8,5,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,10,9,4,3,6,7,8,5,12,11] => {{1,2},{3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [12,5,2,9,4,11,6,7,8,1,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [2,1,12,9,4,11,6,7,8,3,10,5] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [10,5,2,9,4,1,6,7,8,3,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [12,1,10,3,2,5,6,7,8,9,4,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,10,5,6,7,8,9,12,11] => {{1,2},{3,4},{5,6,7,8,9,10},{11,12}}

[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [12,11,2,1,4,5,6,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,12,3,4,5,6,7,8,9,10,11] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [4,1,2,3,10,5,6,7,8,9,12,11] => {{1,2,3,4},{5,6,7,8,9,10},{11,12}}

[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [12,9,2,3,4,11,6,7,8,1,10,5] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,1,4,3,12,11,6,7,8,5,10,9] => {{1,2},{3,4},{5,6,7,8,9,10,11,12}}

[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [10,9,2,3,4,1,6,7,8,5,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [4,1,2,3,12,11,6,7,8,5,10,9] => {{1,2,3,4},{5,6,7,8,9,10,11,12}}

[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [12,1,8,3,4,5,10,7,2,9,6,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,6,3,4,5,8,7,10,9,12,11] => {{1,2},{3,4,5,6},{7,8},{9,10},{11,12}}

[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [12,5,2,11,4,1,10,7,6,9,8,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [2,1,12,11,4,3,10,7,6,9,8,5] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [6,5,2,1,4,3,8,7,10,9,12,11] => {{1,2,3,4,5,6},{7,8},{9,10},{11,12}}

[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [12,11,8,3,4,5,2,7,6,1,10,9] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,6,3,4,5,8,7,12,9,10,11] => {{1,2},{3,4,5,6},{7,8},{9,10,11,12}}

[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [10,1,8,3,4,5,2,7,6,9,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [6,5,2,1,4,3,8,7,12,9,10,11] => {{1,2,3,4,5,6},{7,8},{9,10,11,12}}

[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [12,11,2,3,4,1,10,7,6,9,8,5] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,12,5,10,7,6,9,8,11] => {{1,2},{3,4},{5,6,7,8,9,10,11,12}}

[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [6,1,2,3,4,5,8,7,10,9,12,11] => {{1,2,3,4,5,6},{7,8},{9,10},{11,12}}

[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [4,1,2,3,12,5,10,7,6,9,8,11] => {{1,2,3,4},{5,6,7,8,9,10,11,12}}

[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [6,1,2,3,4,5,8,7,12,9,10,11] => {{1,2,3,4,5,6},{7,8},{9,10,11,12}}

[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [12,1,2,9,4,5,6,3,8,7,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,10,9,4,5,6,3,8,7,12,11] => {{1,2},{3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [12,7,2,9,4,5,6,11,8,1,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [2,1,12,9,4,5,6,11,8,3,10,7] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [10,7,2,9,4,5,6,1,8,3,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [12,1,6,3,10,5,2,7,8,9,4,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,10,7,8,9,12,11] => {{1,2},{3,4},{5,6},{7,8,9,10},{11,12}}

[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [12,11,2,1,10,5,4,7,8,9,6,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,12,3,10,5,4,7,8,9,6,11] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [4,1,2,3,6,5,10,7,8,9,12,11] => {{1,2,3,4},{5,6},{7,8,9,10},{11,12}}

[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [12,9,6,3,2,5,4,11,8,1,10,7] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,1,4,3,6,5,12,11,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8,9,10,11,12}}

[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [10,9,6,3,2,5,4,1,8,7,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [4,1,2,3,6,5,12,11,8,7,10,9] => {{1,2,3,4},{5,6},{7,8,9,10,11,12}}

[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [12,1,10,3,4,5,6,7,2,9,8,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,8,3,4,5,6,7,10,9,12,11] => {{1,2},{3,4,5,6,7,8},{9,10},{11,12}}

[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [12,7,2,11,4,5,6,1,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,12,11,4,5,6,3,8,9,10,7] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [8,7,2,1,4,5,6,3,10,9,12,11] => {{1,2,3,4,5,6,7,8},{9,10},{11,12}}

[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [12,11,2,3,4,5,6,7,8,1,10,9] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,8,3,4,5,6,7,12,9,10,11] => {{1,2},{3,4,5,6,7,8},{9,10,11,12}}

[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,1,2,3,4,5,6,7,8,9,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [8,7,2,1,4,5,6,3,12,9,10,11] => {{1,2,3,4,5,6,7,8},{9,10,11,12}}

[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [12,11,6,3,2,5,4,1,8,9,10,7] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,12,7,8,9,10,11] => {{1,2},{3,4},{5,6},{7,8,9,10,11,12}}

[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [8,1,6,3,2,5,4,7,10,9,12,11] => {{1,2,3,4,5,6,7,8},{9,10},{11,12}}

[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [4,1,2,3,6,5,12,7,8,9,10,11] => {{1,2,3,4},{5,6},{7,8,9,10,11,12}}

[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [8,1,6,3,2,5,4,7,12,9,10,11] => {{1,2,3,4,5,6,7,8},{9,10,11,12}}

[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [12,1,10,3,4,5,2,7,8,9,6,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,6,3,4,5,10,7,8,9,12,11] => {{1,2},{3,4,5,6},{7,8,9,10},{11,12}}

[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [12,5,2,11,4,1,6,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,12,11,4,3,6,7,8,9,10,5] => {{1,2},{3,4,5,6,7,8,9,10,11,12}}

[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [6,5,2,1,4,3,10,7,8,9,12,11] => {{1,2,3,4,5,6},{7,8,9,10},{11,12}}

[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [12,9,2,3,4,5,6,11,8,1,10,7] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,6,3,4,5,12,11,8,7,10,9] => {{1,2},{3,4,5,6},{7,8,9,10,11,12}}

[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [10,9,2,3,4,5,6,1,8,7,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [6,5,2,1,4,3,12,11,8,7,10,9] => {{1,2,3,4,5,6},{7,8,9,10,11,12}}

[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [12,11,2,3,4,1,6,7,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,12,5,6,7,8,9,10,11] => {{1,2},{3,4},{5,6,7,8,9,10,11,12}}

[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [6,1,2,3,4,5,10,7,8,9,12,11] => {{1,2,3,4,5,6},{7,8,9,10},{11,12}}

[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [4,1,2,3,12,5,6,7,8,9,10,11] => {{1,2,3,4},{5,6,7,8,9,10,11,12}}

[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [6,1,2,3,4,5,12,11,8,7,10,9] => {{1,2,3,4,5,6},{7,8,9,10,11,12}}

[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [12,11,2,3,4,5,6,1,8,9,10,7] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,6,3,4,5,12,7,8,9,10,11] => {{1,2},{3,4,5,6},{7,8,9,10,11,12}}

[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [8,1,2,3,4,5,6,7,10,9,12,11] => {{1,2,3,4,5,6,7,8},{9,10},{11,12}}

[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [6,5,2,1,4,3,12,7,8,9,10,11] => {{1,2,3,4,5,6},{7,8,9,10,11,12}}

[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [8,1,2,3,4,5,6,7,12,9,10,11] => {{1,2,3,4,5,6,7,8},{9,10,11,12}}

[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [6,1,2,3,4,5,12,7,8,9,10,11] => {{1,2,3,4,5,6},{7,8,9,10,11,12}}

[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,10,12,11,9] => {{1,2},{3,4},{5,6},{7,8},{9,10,12},{11}}

[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,8,10,9,7,12,11] => {{1,2},{3,4},{5,6},{7,8,10},{9},{11,12}}

[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,8,9,12,10,11,7] => {{1,2},{3,4},{5,6},{7,8,9,12},{10},{11}}

[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,6,8,7,5,10,9,12,11] => {{1,2},{3,4},{5,6,8},{7},{9,10},{11,12}}

[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,6,8,7,5,10,12,11,9] => {{1,2},{3,4},{5,6,8},{7},{9,10,12},{11}}

[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,6,7,10,8,9,5,12,11] => {{1,2},{3,4},{5,6,7,10},{8},{9},{11,12}}

[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,6,7,8,12,9,10,11,5] => {{1,2},{3,4},{5,6,7,8,12},{9},{10},{11}}

[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,4,6,5,3,8,7,10,9,12,11] => {{1,2},{3,4,6},{5},{7,8},{9,10},{11,12}}

[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,4,6,5,3,8,7,10,12,11,9] => {{1,2},{3,4,6},{5},{7,8},{9,10,12},{11}}

[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,4,6,5,3,8,10,9,7,12,11] => {{1,2},{3,4,6},{5},{7,8,10},{9},{11,12}}

[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,4,6,5,3,8,9,12,10,11,7] => {{1,2},{3,4,6},{5},{7,8,9,12},{10},{11}}

[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,4,5,8,6,7,3,10,9,12,11] => {{1,2},{3,4,5,8},{6},{7},{9,10},{11,12}}

[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,4,5,8,6,7,3,10,12,11,9] => {{1,2},{3,4,5,8},{6},{7},{9,10,12},{11}}

[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,4,5,6,10,7,8,9,3,12,11] => {{1,2},{3,4,5,6,10},{7},{8},{9},{11,12}}

[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,4,5,6,7,12,8,9,10,11,3] => {{1,2},{3,4,5,6,7,12},{8},{9},{10},{11}}

[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [2,4,3,1,6,5,8,7,10,9,12,11] => {{1,2,4},{3},{5,6},{7,8},{9,10},{11,12}}

[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [2,4,3,1,6,5,8,7,10,12,11,9] => {{1,2,4},{3},{5,6},{7,8},{9,10,12},{11}}

[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [2,4,3,1,6,5,8,10,9,7,12,11] => {{1,2,4},{3},{5,6},{7,8,10},{9},{11,12}}

[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [2,4,3,1,6,5,8,9,12,10,11,7] => {{1,2,4},{3},{5,6},{7,8,9,12},{10},{11}}

[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [2,4,3,1,6,8,7,5,10,9,12,11] => {{1,2,4},{3},{5,6,8},{7},{9,10},{11,12}}

[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [2,4,3,1,6,8,7,5,10,12,11,9] => {{1,2,4},{3},{5,6,8},{7},{9,10,12},{11}}

[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [2,4,3,1,6,7,10,8,9,5,12,11] => {{1,2,4},{3},{5,6,7,10},{8},{9},{11,12}}

[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [2,4,3,1,6,7,8,12,9,10,11,5] => {{1,2,4},{3},{5,6,7,8,12},{9},{10},{11}}

[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [2,3,6,4,5,1,8,7,10,9,12,11] => {{1,2,3,6},{4},{5},{7,8},{9,10},{11,12}}

[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [2,3,6,4,5,1,8,7,10,12,11,9] => {{1,2,3,6},{4},{5},{7,8},{9,10,12},{11}}

[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [2,3,6,4,5,1,8,10,9,7,12,11] => {{1,2,3,6},{4},{5},{7,8,10},{9},{11,12}}

[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [2,3,6,4,5,1,8,9,12,10,11,7] => {{1,2,3,6},{4},{5},{7,8,9,12},{10},{11}}

[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [2,3,4,8,5,6,7,1,10,9,12,11] => {{1,2,3,4,8},{5},{6},{7},{9,10},{11,12}}

[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [2,3,4,8,5,6,7,1,10,12,11,9] => {{1,2,3,4,8},{5},{6},{7},{9,10,12},{11}}

[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [2,3,4,5,10,6,7,8,9,1,12,11] => {{1,2,3,4,5,10},{6},{7},{8},{9},{11,12}}

[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [2,3,4,5,6,12,7,8,9,10,11,1] => {{1,2,3,4,5,6,12},{7},{8},{9},{10},{11}}

Map

to permutation

Description

Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.

Map

first fundamental transformation

Description

Return the permutation whose cycles are the subsequences between successive left to right maxima.

Map

to cycle type

Description

Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].