- FindStat

Identifier

Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 127 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Map

to permutation

Description

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

Map

Inverse Kreweras complement

Description

Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.

Map

weak exceedance partition

Description

The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.