Identifier
Mp00092:
Perfect matchings
—to set partition⟶
Set partitions
Mp00112: Set partitions —complement⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00112: Set partitions —complement⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Images
[(1,2)] => {{1,2}} => {{1,2}} => [2,1]
[(1,2),(3,4)] => {{1,2},{3,4}} => {{1,2},{3,4}} => [2,1,4,3]
[(1,3),(2,4)] => {{1,3},{2,4}} => {{1,3},{2,4}} => [3,4,1,2]
[(1,4),(2,3)] => {{1,4},{2,3}} => {{1,4},{2,3}} => [4,3,2,1]
[(1,2),(3,4),(5,6)] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5]
[(1,3),(2,4),(5,6)] => {{1,3},{2,4},{5,6}} => {{1,2},{3,5},{4,6}} => [2,1,5,6,3,4]
[(1,4),(2,3),(5,6)] => {{1,4},{2,3},{5,6}} => {{1,2},{3,6},{4,5}} => [2,1,6,5,4,3]
[(1,5),(2,3),(4,6)] => {{1,5},{2,3},{4,6}} => {{1,3},{2,6},{4,5}} => [3,6,1,5,4,2]
[(1,6),(2,3),(4,5)] => {{1,6},{2,3},{4,5}} => {{1,6},{2,3},{4,5}} => [6,3,2,5,4,1]
[(1,6),(2,4),(3,5)] => {{1,6},{2,4},{3,5}} => {{1,6},{2,4},{3,5}} => [6,4,5,2,3,1]
[(1,5),(2,4),(3,6)] => {{1,5},{2,4},{3,6}} => {{1,4},{2,6},{3,5}} => [4,6,5,1,3,2]
[(1,4),(2,5),(3,6)] => {{1,4},{2,5},{3,6}} => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3]
[(1,3),(2,5),(4,6)] => {{1,3},{2,5},{4,6}} => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4]
[(1,2),(3,5),(4,6)] => {{1,2},{3,5},{4,6}} => {{1,3},{2,4},{5,6}} => [3,4,1,2,6,5]
[(1,2),(3,6),(4,5)] => {{1,2},{3,6},{4,5}} => {{1,4},{2,3},{5,6}} => [4,3,2,1,6,5]
[(1,3),(2,6),(4,5)] => {{1,3},{2,6},{4,5}} => {{1,5},{2,3},{4,6}} => [5,3,2,6,1,4]
[(1,4),(2,6),(3,5)] => {{1,4},{2,6},{3,5}} => {{1,5},{2,4},{3,6}} => [5,4,6,2,1,3]
[(1,5),(2,6),(3,4)] => {{1,5},{2,6},{3,4}} => {{1,5},{2,6},{3,4}} => [5,6,4,3,1,2]
[(1,6),(2,5),(3,4)] => {{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1]
[(1,2),(3,4),(5,6),(7,8)] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7]
[(1,3),(2,4),(5,6),(7,8)] => {{1,3},{2,4},{5,6},{7,8}} => {{1,2},{3,4},{5,7},{6,8}} => [2,1,4,3,7,8,5,6]
[(1,4),(2,3),(5,6),(7,8)] => {{1,4},{2,3},{5,6},{7,8}} => {{1,2},{3,4},{5,8},{6,7}} => [2,1,4,3,8,7,6,5]
[(1,5),(2,3),(4,6),(7,8)] => {{1,5},{2,3},{4,6},{7,8}} => {{1,2},{3,5},{4,8},{6,7}} => [2,1,5,8,3,7,6,4]
[(1,6),(2,3),(4,5),(7,8)] => {{1,6},{2,3},{4,5},{7,8}} => {{1,2},{3,8},{4,5},{6,7}} => [2,1,8,5,4,7,6,3]
[(1,7),(2,3),(4,5),(6,8)] => {{1,7},{2,3},{4,5},{6,8}} => {{1,3},{2,8},{4,5},{6,7}} => [3,8,1,5,4,7,6,2]
[(1,8),(2,3),(4,5),(6,7)] => {{1,8},{2,3},{4,5},{6,7}} => {{1,8},{2,3},{4,5},{6,7}} => [8,3,2,5,4,7,6,1]
[(1,8),(2,4),(3,5),(6,7)] => {{1,8},{2,4},{3,5},{6,7}} => {{1,8},{2,3},{4,6},{5,7}} => [8,3,2,6,7,4,5,1]
[(1,7),(2,4),(3,5),(6,8)] => {{1,7},{2,4},{3,5},{6,8}} => {{1,3},{2,8},{4,6},{5,7}} => [3,8,1,6,7,4,5,2]
[(1,6),(2,4),(3,5),(7,8)] => {{1,6},{2,4},{3,5},{7,8}} => {{1,2},{3,8},{4,6},{5,7}} => [2,1,8,6,7,4,5,3]
[(1,5),(2,4),(3,6),(7,8)] => {{1,5},{2,4},{3,6},{7,8}} => {{1,2},{3,6},{4,8},{5,7}} => [2,1,6,8,7,3,5,4]
[(1,4),(2,5),(3,6),(7,8)] => {{1,4},{2,5},{3,6},{7,8}} => {{1,2},{3,6},{4,7},{5,8}} => [2,1,6,7,8,3,4,5]
[(1,3),(2,5),(4,6),(7,8)] => {{1,3},{2,5},{4,6},{7,8}} => {{1,2},{3,5},{4,7},{6,8}} => [2,1,5,7,3,8,4,6]
[(1,2),(3,5),(4,6),(7,8)] => {{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6},{7,8}} => [2,1,5,6,3,4,8,7]
[(1,2),(3,6),(4,5),(7,8)] => {{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5},{7,8}} => [2,1,6,5,4,3,8,7]
[(1,3),(2,6),(4,5),(7,8)] => {{1,3},{2,6},{4,5},{7,8}} => {{1,2},{3,7},{4,5},{6,8}} => [2,1,7,5,4,8,3,6]
[(1,4),(2,6),(3,5),(7,8)] => {{1,4},{2,6},{3,5},{7,8}} => {{1,2},{3,7},{4,6},{5,8}} => [2,1,7,6,8,4,3,5]
[(1,5),(2,6),(3,4),(7,8)] => {{1,5},{2,6},{3,4},{7,8}} => {{1,2},{3,7},{4,8},{5,6}} => [2,1,7,8,6,5,3,4]
[(1,6),(2,5),(3,4),(7,8)] => {{1,6},{2,5},{3,4},{7,8}} => {{1,2},{3,8},{4,7},{5,6}} => [2,1,8,7,6,5,4,3]
[(1,7),(2,5),(3,4),(6,8)] => {{1,7},{2,5},{3,4},{6,8}} => {{1,3},{2,8},{4,7},{5,6}} => [3,8,1,7,6,5,4,2]
[(1,8),(2,5),(3,4),(6,7)] => {{1,8},{2,5},{3,4},{6,7}} => {{1,8},{2,3},{4,7},{5,6}} => [8,3,2,7,6,5,4,1]
[(1,8),(2,6),(3,4),(5,7)] => {{1,8},{2,6},{3,4},{5,7}} => {{1,8},{2,4},{3,7},{5,6}} => [8,4,7,2,6,5,3,1]
[(1,7),(2,6),(3,4),(5,8)] => {{1,7},{2,6},{3,4},{5,8}} => {{1,4},{2,8},{3,7},{5,6}} => [4,8,7,1,6,5,3,2]
[(1,6),(2,7),(3,4),(5,8)] => {{1,6},{2,7},{3,4},{5,8}} => {{1,4},{2,7},{3,8},{5,6}} => [4,7,8,1,6,5,2,3]
[(1,5),(2,7),(3,4),(6,8)] => {{1,5},{2,7},{3,4},{6,8}} => {{1,3},{2,7},{4,8},{5,6}} => [3,7,1,8,6,5,2,4]
[(1,4),(2,7),(3,5),(6,8)] => {{1,4},{2,7},{3,5},{6,8}} => {{1,3},{2,7},{4,6},{5,8}} => [3,7,1,6,8,4,2,5]
[(1,3),(2,7),(4,5),(6,8)] => {{1,3},{2,7},{4,5},{6,8}} => {{1,3},{2,7},{4,5},{6,8}} => [3,7,1,5,4,8,2,6]
[(1,2),(3,7),(4,5),(6,8)] => {{1,2},{3,7},{4,5},{6,8}} => {{1,3},{2,6},{4,5},{7,8}} => [3,6,1,5,4,2,8,7]
[(1,2),(3,8),(4,5),(6,7)] => {{1,2},{3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5},{7,8}} => [6,3,2,5,4,1,8,7]
[(1,3),(2,8),(4,5),(6,7)] => {{1,3},{2,8},{4,5},{6,7}} => {{1,7},{2,3},{4,5},{6,8}} => [7,3,2,5,4,8,1,6]
[(1,4),(2,8),(3,5),(6,7)] => {{1,4},{2,8},{3,5},{6,7}} => {{1,7},{2,3},{4,6},{5,8}} => [7,3,2,6,8,4,1,5]
[(1,5),(2,8),(3,4),(6,7)] => {{1,5},{2,8},{3,4},{6,7}} => {{1,7},{2,3},{4,8},{5,6}} => [7,3,2,8,6,5,1,4]
[(1,6),(2,8),(3,4),(5,7)] => {{1,6},{2,8},{3,4},{5,7}} => {{1,7},{2,4},{3,8},{5,6}} => [7,4,8,2,6,5,1,3]
[(1,7),(2,8),(3,4),(5,6)] => {{1,7},{2,8},{3,4},{5,6}} => {{1,7},{2,8},{3,4},{5,6}} => [7,8,4,3,6,5,1,2]
[(1,8),(2,7),(3,4),(5,6)] => {{1,8},{2,7},{3,4},{5,6}} => {{1,8},{2,7},{3,4},{5,6}} => [8,7,4,3,6,5,2,1]
[(1,8),(2,7),(3,5),(4,6)] => {{1,8},{2,7},{3,5},{4,6}} => {{1,8},{2,7},{3,5},{4,6}} => [8,7,5,6,3,4,2,1]
[(1,7),(2,8),(3,5),(4,6)] => {{1,7},{2,8},{3,5},{4,6}} => {{1,7},{2,8},{3,5},{4,6}} => [7,8,5,6,3,4,1,2]
[(1,6),(2,8),(3,5),(4,7)] => {{1,6},{2,8},{3,5},{4,7}} => {{1,7},{2,5},{3,8},{4,6}} => [7,5,8,6,2,4,1,3]
[(1,5),(2,8),(3,6),(4,7)] => {{1,5},{2,8},{3,6},{4,7}} => {{1,7},{2,5},{3,6},{4,8}} => [7,5,6,8,2,3,1,4]
[(1,4),(2,8),(3,6),(5,7)] => {{1,4},{2,8},{3,6},{5,7}} => {{1,7},{2,4},{3,6},{5,8}} => [7,4,6,2,8,3,1,5]
[(1,3),(2,8),(4,6),(5,7)] => {{1,3},{2,8},{4,6},{5,7}} => {{1,7},{2,4},{3,5},{6,8}} => [7,4,5,2,3,8,1,6]
[(1,2),(3,8),(4,6),(5,7)] => {{1,2},{3,8},{4,6},{5,7}} => {{1,6},{2,4},{3,5},{7,8}} => [6,4,5,2,3,1,8,7]
[(1,2),(3,7),(4,6),(5,8)] => {{1,2},{3,7},{4,6},{5,8}} => {{1,4},{2,6},{3,5},{7,8}} => [4,6,5,1,3,2,8,7]
[(1,3),(2,7),(4,6),(5,8)] => {{1,3},{2,7},{4,6},{5,8}} => {{1,4},{2,7},{3,5},{6,8}} => [4,7,5,1,3,8,2,6]
[(1,4),(2,7),(3,6),(5,8)] => {{1,4},{2,7},{3,6},{5,8}} => {{1,4},{2,7},{3,6},{5,8}} => [4,7,6,1,8,3,2,5]
[(1,5),(2,7),(3,6),(4,8)] => {{1,5},{2,7},{3,6},{4,8}} => {{1,5},{2,7},{3,6},{4,8}} => [5,7,6,8,1,3,2,4]
[(1,6),(2,7),(3,5),(4,8)] => {{1,6},{2,7},{3,5},{4,8}} => {{1,5},{2,7},{3,8},{4,6}} => [5,7,8,6,1,4,2,3]
[(1,7),(2,6),(3,5),(4,8)] => {{1,7},{2,6},{3,5},{4,8}} => {{1,5},{2,8},{3,7},{4,6}} => [5,8,7,6,1,4,3,2]
[(1,8),(2,6),(3,5),(4,7)] => {{1,8},{2,6},{3,5},{4,7}} => {{1,8},{2,5},{3,7},{4,6}} => [8,5,7,6,2,4,3,1]
[(1,8),(2,5),(3,6),(4,7)] => {{1,8},{2,5},{3,6},{4,7}} => {{1,8},{2,5},{3,6},{4,7}} => [8,5,6,7,2,3,4,1]
[(1,7),(2,5),(3,6),(4,8)] => {{1,7},{2,5},{3,6},{4,8}} => {{1,5},{2,8},{3,6},{4,7}} => [5,8,6,7,1,3,4,2]
[(1,6),(2,5),(3,7),(4,8)] => {{1,6},{2,5},{3,7},{4,8}} => {{1,5},{2,6},{3,8},{4,7}} => [5,6,8,7,1,2,4,3]
[(1,5),(2,6),(3,7),(4,8)] => {{1,5},{2,6},{3,7},{4,8}} => {{1,5},{2,6},{3,7},{4,8}} => [5,6,7,8,1,2,3,4]
[(1,4),(2,6),(3,7),(5,8)] => {{1,4},{2,6},{3,7},{5,8}} => {{1,4},{2,6},{3,7},{5,8}} => [4,6,7,1,8,2,3,5]
[(1,3),(2,6),(4,7),(5,8)] => {{1,3},{2,6},{4,7},{5,8}} => {{1,4},{2,5},{3,7},{6,8}} => [4,5,7,1,2,8,3,6]
[(1,2),(3,6),(4,7),(5,8)] => {{1,2},{3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6},{7,8}} => [4,5,6,1,2,3,8,7]
[(1,2),(3,5),(4,7),(6,8)] => {{1,2},{3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6},{7,8}} => [3,5,1,6,2,4,8,7]
[(1,3),(2,5),(4,7),(6,8)] => {{1,3},{2,5},{4,7},{6,8}} => {{1,3},{2,5},{4,7},{6,8}} => [3,5,1,7,2,8,4,6]
[(1,4),(2,5),(3,7),(6,8)] => {{1,4},{2,5},{3,7},{6,8}} => {{1,3},{2,6},{4,7},{5,8}} => [3,6,1,7,8,2,4,5]
[(1,5),(2,4),(3,7),(6,8)] => {{1,5},{2,4},{3,7},{6,8}} => {{1,3},{2,6},{4,8},{5,7}} => [3,6,1,8,7,2,5,4]
[(1,6),(2,4),(3,7),(5,8)] => {{1,6},{2,4},{3,7},{5,8}} => {{1,4},{2,6},{3,8},{5,7}} => [4,6,8,1,7,2,5,3]
[(1,7),(2,4),(3,6),(5,8)] => {{1,7},{2,4},{3,6},{5,8}} => {{1,4},{2,8},{3,6},{5,7}} => [4,8,6,1,7,3,5,2]
[(1,8),(2,4),(3,6),(5,7)] => {{1,8},{2,4},{3,6},{5,7}} => {{1,8},{2,4},{3,6},{5,7}} => [8,4,6,2,7,3,5,1]
[(1,8),(2,3),(4,6),(5,7)] => {{1,8},{2,3},{4,6},{5,7}} => {{1,8},{2,4},{3,5},{6,7}} => [8,4,5,2,3,7,6,1]
[(1,7),(2,3),(4,6),(5,8)] => {{1,7},{2,3},{4,6},{5,8}} => {{1,4},{2,8},{3,5},{6,7}} => [4,8,5,1,3,7,6,2]
[(1,6),(2,3),(4,7),(5,8)] => {{1,6},{2,3},{4,7},{5,8}} => {{1,4},{2,5},{3,8},{6,7}} => [4,5,8,1,2,7,6,3]
[(1,5),(2,3),(4,7),(6,8)] => {{1,5},{2,3},{4,7},{6,8}} => {{1,3},{2,5},{4,8},{6,7}} => [3,5,1,8,2,7,6,4]
[(1,4),(2,3),(5,7),(6,8)] => {{1,4},{2,3},{5,7},{6,8}} => {{1,3},{2,4},{5,8},{6,7}} => [3,4,1,2,8,7,6,5]
[(1,3),(2,4),(5,7),(6,8)] => {{1,3},{2,4},{5,7},{6,8}} => {{1,3},{2,4},{5,7},{6,8}} => [3,4,1,2,7,8,5,6]
[(1,2),(3,4),(5,7),(6,8)] => {{1,2},{3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6},{7,8}} => [3,4,1,2,6,5,8,7]
[(1,2),(3,4),(5,8),(6,7)] => {{1,2},{3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6},{7,8}} => [4,3,2,1,6,5,8,7]
[(1,3),(2,4),(5,8),(6,7)] => {{1,3},{2,4},{5,8},{6,7}} => {{1,4},{2,3},{5,7},{6,8}} => [4,3,2,1,7,8,5,6]
[(1,4),(2,3),(5,8),(6,7)] => {{1,4},{2,3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6,7}} => [4,3,2,1,8,7,6,5]
[(1,5),(2,3),(4,8),(6,7)] => {{1,5},{2,3},{4,8},{6,7}} => {{1,5},{2,3},{4,8},{6,7}} => [5,3,2,8,1,7,6,4]
[(1,6),(2,3),(4,8),(5,7)] => {{1,6},{2,3},{4,8},{5,7}} => {{1,5},{2,4},{3,8},{6,7}} => [5,4,8,2,1,7,6,3]
[(1,7),(2,3),(4,8),(5,6)] => {{1,7},{2,3},{4,8},{5,6}} => {{1,5},{2,8},{3,4},{6,7}} => [5,8,4,3,1,7,6,2]
[(1,8),(2,3),(4,7),(5,6)] => {{1,8},{2,3},{4,7},{5,6}} => {{1,8},{2,5},{3,4},{6,7}} => [8,5,4,3,2,7,6,1]
[(1,8),(2,4),(3,7),(5,6)] => {{1,8},{2,4},{3,7},{5,6}} => {{1,8},{2,6},{3,4},{5,7}} => [8,6,4,3,7,2,5,1]
[(1,7),(2,4),(3,8),(5,6)] => {{1,7},{2,4},{3,8},{5,6}} => {{1,6},{2,8},{3,4},{5,7}} => [6,8,4,3,7,1,5,2]
[(1,6),(2,4),(3,8),(5,7)] => {{1,6},{2,4},{3,8},{5,7}} => {{1,6},{2,4},{3,8},{5,7}} => [6,4,8,2,7,1,5,3]
[(1,5),(2,4),(3,8),(6,7)] => {{1,5},{2,4},{3,8},{6,7}} => {{1,6},{2,3},{4,8},{5,7}} => [6,3,2,8,7,1,5,4]
[(1,4),(2,5),(3,8),(6,7)] => {{1,4},{2,5},{3,8},{6,7}} => {{1,6},{2,3},{4,7},{5,8}} => [6,3,2,7,8,1,4,5]
>>> Load all 126 entries. <<<Map
to set partition
Description
Return the set partition corresponding to the perfect matching.
Map
complement
Description
The complement of a set partition obtained by replacing $i$ with $n+1-i$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
searching the database
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