Identifier
Values
[(1,2)] => {{1,2}} => {{1},{2}} => 1
[(1,2),(3,4)] => {{1,2},{3,4}} => {{1,3},{2},{4}} => 2
[(1,3),(2,4)] => {{1,3},{2,4}} => {{1,3},{2,4}} => 1
[(1,4),(2,3)] => {{1,4},{2,3}} => {{1},{2,4},{3}} => 2
[(1,2),(3,4),(5,6)] => {{1,2},{3,4},{5,6}} => {{1,3,5},{2},{4},{6}} => 2
[(1,3),(2,4),(5,6)] => {{1,3},{2,4},{5,6}} => {{1,3,5},{2},{4,6}} => 6
[(1,4),(2,3),(5,6)] => {{1,4},{2,3},{5,6}} => {{1,3},{2},{4,6},{5}} => 3
[(1,5),(2,3),(4,6)] => {{1,5},{2,3},{4,6}} => {{1,3},{2,4,6},{5}} => 6
[(1,6),(2,3),(4,5)] => {{1,6},{2,3},{4,5}} => {{1},{2,4,6},{3},{5}} => 2
[(1,6),(2,4),(3,5)] => {{1,6},{2,4},{3,5}} => {{1},{2,4,6},{3,5}} => 6
[(1,5),(2,4),(3,6)] => {{1,5},{2,4},{3,6}} => {{1,4},{2,6},{3,5}} => 3
[(1,4),(2,5),(3,6)] => {{1,4},{2,5},{3,6}} => {{1,4},{2,5},{3,6}} => 1
[(1,3),(2,5),(4,6)] => {{1,3},{2,5},{4,6}} => {{1,3},{2,5},{4,6}} => 3
[(1,2),(3,5),(4,6)] => {{1,2},{3,5},{4,6}} => {{1,3,5},{2,4},{6}} => 6
[(1,2),(3,6),(4,5)] => {{1,2},{3,6},{4,5}} => {{1,5},{2,4},{3},{6}} => 3
[(1,3),(2,6),(4,5)] => {{1,3},{2,6},{4,5}} => {{1,5},{2,4,6},{3}} => 6
[(1,4),(2,6),(3,5)] => {{1,4},{2,6},{3,5}} => {{1,5},{2,4},{3,6}} => 3
[(1,5),(2,6),(3,4)] => {{1,5},{2,6},{3,4}} => {{1,3,5},{2,6},{4}} => 6
[(1,6),(2,5),(3,4)] => {{1,6},{2,5},{3,4}} => {{1},{2,6},{3,5},{4}} => 3
[(1,7),(2,4),(3,5),(6,8)] => {{1,7},{2,4},{3,5},{6,8}} => {{1,3},{2,8},{4,6},{5,7}} => 4
[(1,4),(2,7),(3,5),(6,8)] => {{1,4},{2,7},{3,5},{6,8}} => {{1,3},{2,7},{4,6},{5,8}} => 8
[(1,7),(2,8),(3,5),(4,6)] => {{1,7},{2,8},{3,5},{4,6}} => {{1,7},{2,8},{3,5},{4,6}} => 4
[(1,6),(2,8),(3,5),(4,7)] => {{1,6},{2,8},{3,5},{4,7}} => {{1,7},{2,5},{3,8},{4,6}} => 8
[(1,5),(2,8),(3,6),(4,7)] => {{1,5},{2,8},{3,6},{4,7}} => {{1,7},{2,5},{3,6},{4,8}} => 8
[(1,4),(2,8),(3,6),(5,7)] => {{1,4},{2,8},{3,6},{5,7}} => {{1,7},{2,4},{3,6},{5,8}} => 8
[(1,3),(2,8),(4,6),(5,7)] => {{1,3},{2,8},{4,6},{5,7}} => {{1,7},{2,4},{3,5},{6,8}} => 4
[(1,3),(2,7),(4,6),(5,8)] => {{1,3},{2,7},{4,6},{5,8}} => {{1,4},{2,7},{3,5},{6,8}} => 8
[(1,4),(2,7),(3,6),(5,8)] => {{1,4},{2,7},{3,6},{5,8}} => {{1,4},{2,7},{3,6},{5,8}} => 2
[(1,5),(2,7),(3,6),(4,8)] => {{1,5},{2,7},{3,6},{4,8}} => {{1,5},{2,7},{3,6},{4,8}} => 4
[(1,6),(2,7),(3,5),(4,8)] => {{1,6},{2,7},{3,5},{4,8}} => {{1,5},{2,7},{3,8},{4,6}} => 8
[(1,7),(2,6),(3,5),(4,8)] => {{1,7},{2,6},{3,5},{4,8}} => {{1,5},{2,8},{3,7},{4,6}} => 4
[(1,7),(2,5),(3,6),(4,8)] => {{1,7},{2,5},{3,6},{4,8}} => {{1,5},{2,8},{3,6},{4,7}} => 8
[(1,6),(2,5),(3,7),(4,8)] => {{1,6},{2,5},{3,7},{4,8}} => {{1,5},{2,6},{3,8},{4,7}} => 4
[(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
[(1,4),(2,6),(3,7),(5,8)] => {{1,4},{2,6},{3,7},{5,8}} => {{1,4},{2,6},{3,7},{5,8}} => 4
[(1,3),(2,6),(4,7),(5,8)] => {{1,3},{2,6},{4,7},{5,8}} => {{1,4},{2,5},{3,7},{6,8}} => 8
[(1,3),(2,5),(4,7),(6,8)] => {{1,3},{2,5},{4,7},{6,8}} => {{1,3},{2,5},{4,7},{6,8}} => 8
[(1,4),(2,5),(3,7),(6,8)] => {{1,4},{2,5},{3,7},{6,8}} => {{1,3},{2,6},{4,7},{5,8}} => 8
[(1,5),(2,4),(3,7),(6,8)] => {{1,5},{2,4},{3,7},{6,8}} => {{1,3},{2,6},{4,8},{5,7}} => 4
[(1,6),(2,4),(3,7),(5,8)] => {{1,6},{2,4},{3,7},{5,8}} => {{1,4},{2,6},{3,8},{5,7}} => 8
[(1,7),(2,4),(3,6),(5,8)] => {{1,7},{2,4},{3,6},{5,8}} => {{1,4},{2,8},{3,6},{5,7}} => 8
[(1,3),(2,4),(5,7),(6,8)] => {{1,3},{2,4},{5,7},{6,8}} => {{1,3},{2,4},{5,7},{6,8}} => 4
[(1,6),(2,4),(3,8),(5,7)] => {{1,6},{2,4},{3,8},{5,7}} => {{1,6},{2,4},{3,8},{5,7}} => 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}} => 4
[(1,4),(2,6),(3,8),(5,7)] => {{1,4},{2,6},{3,8},{5,7}} => {{1,6},{2,4},{3,7},{5,8}} => 8
[(1,5),(2,6),(3,8),(4,7)] => {{1,5},{2,6},{3,8},{4,7}} => {{1,6},{2,5},{3,7},{4,8}} => 4
[(1,6),(2,5),(3,8),(4,7)] => {{1,6},{2,5},{3,8},{4,7}} => {{1,6},{2,5},{3,8},{4,7}} => 2
[(1,7),(2,5),(3,8),(4,6)] => {{1,7},{2,5},{3,8},{4,6}} => {{1,6},{2,8},{3,5},{4,7}} => 8
[(1,5),(2,7),(3,8),(4,6)] => {{1,5},{2,7},{3,8},{4,6}} => {{1,6},{2,7},{3,5},{4,8}} => 8
[(1,5),(2,8),(3,7),(4,6)] => {{1,5},{2,8},{3,7},{4,6}} => {{1,7},{2,6},{3,5},{4,8}} => 4
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Description
The size of the orbit of the set partition under rotation.
Map
to set partition
Description
Return the set partition corresponding to the perfect matching.
Map
conjugate
Description
The conjugate of a set partition.
This is an involution exchanging singletons and circular adjacencies due to [1].