- FindStat

Identifier

Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00091: Set partitions —rotate increasing⟶ Set partitions
Mp00249: Set partitions —Callan switch⟶ Set partitions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 124 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Map

to set partition

Description

Return the set partition corresponding to the perfect matching.

Map

rotate increasing

Description

The rotation of the set partition obtained by adding 1 to each entry different from the largest, and replacing the largest entry with 1.

Map

Callan switch

Description

Switch the first closer and the minimum of the smallest closer and the second element of the block containing 1 in a set partition.
More precisely, this involution implements a joint symmetry between St000971The smallest closer of a set partition. and St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition..