Identifier
Mp00283: Perfect matchings non-nesting-exceedence permutationPermutations
Mp00240: Permutations weak exceedance partitionSet partitions
Mp00164: Set partitions Chen Deng Du Stanley Yan Set partitions
Images
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Cc0012;cc-rep-0Cc0009;cc-rep-2Cc0009;cc-rep-3
[(1,2)]=>[2,1]=>{{1,2}}=>{{1,2}} [(1,2),(3,4)]=>[2,1,4,3]=>{{1,2},{3,4}}=>{{1,2},{3,4}} [(1,3),(2,4)]=>[3,4,1,2]=>{{1,3},{2,4}}=>{{1,4},{2,3}} [(1,4),(2,3)]=>[3,4,2,1]=>{{1,3},{2,4}}=>{{1,4},{2,3}} [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>{{1,2},{3,4},{5,6}} [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3},{5,6}} [(1,4),(2,3),(5,6)]=>[3,4,2,1,6,5]=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3},{5,6}} [(1,5),(2,3),(4,6)]=>[3,5,2,6,1,4]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}} [(1,6),(2,3),(4,5)]=>[3,5,2,6,4,1]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}} [(1,6),(2,4),(3,5)]=>[4,5,6,2,3,1]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}} [(1,5),(2,4),(3,6)]=>[4,5,6,2,1,3]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}} [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}} [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}} [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}=>{{1,2},{3,6},{4,5}} [(1,2),(3,6),(4,5)]=>[2,1,5,6,4,3]=>{{1,2},{3,5},{4,6}}=>{{1,2},{3,6},{4,5}} [(1,3),(2,6),(4,5)]=>[3,5,1,6,4,2]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3},{4,5}} [(1,4),(2,6),(3,5)]=>[4,5,6,1,3,2]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}} [(1,5),(2,6),(3,4)]=>[4,5,6,3,1,2]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}} [(1,6),(2,5),(3,4)]=>[4,5,6,3,2,1]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}} [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2},{3,4},{5,6},{7,8}} [(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>{{1,4},{2,3},{5,6},{7,8}} [(1,4),(2,3),(5,6),(7,8)]=>[3,4,2,1,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>{{1,4},{2,3},{5,6},{7,8}} [(1,5),(2,3),(4,6),(7,8)]=>[3,5,2,6,1,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3},{4,5},{7,8}} [(1,6),(2,3),(4,5),(7,8)]=>[3,5,2,6,4,1,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3},{4,5},{7,8}} [(1,7),(2,3),(4,5),(6,8)]=>[3,5,2,7,4,8,1,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [(1,8),(2,3),(4,5),(6,7)]=>[3,5,2,7,4,8,6,1]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [(1,8),(2,4),(3,5),(6,7)]=>[4,5,7,2,3,8,6,1]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,7),(2,4),(3,5),(6,8)]=>[4,5,7,2,3,8,1,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,6),(2,4),(3,5),(7,8)]=>[4,5,6,2,3,1,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}} [(1,5),(2,4),(3,6),(7,8)]=>[4,5,6,2,1,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}} [(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}} [(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3},{4,5},{7,8}} [(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>{{1,2},{3,6},{4,5},{7,8}} [(1,2),(3,6),(4,5),(7,8)]=>[2,1,5,6,4,3,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>{{1,2},{3,6},{4,5},{7,8}} [(1,3),(2,6),(4,5),(7,8)]=>[3,5,1,6,4,2,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3},{4,5},{7,8}} [(1,4),(2,6),(3,5),(7,8)]=>[4,5,6,1,3,2,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}} [(1,5),(2,6),(3,4),(7,8)]=>[4,5,6,3,1,2,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}} [(1,6),(2,5),(3,4),(7,8)]=>[4,5,6,3,2,1,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4},{7,8}} [(1,7),(2,5),(3,4),(6,8)]=>[4,5,7,3,2,8,1,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,8),(2,5),(3,4),(6,7)]=>[4,5,7,3,2,8,6,1]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,8),(2,6),(3,4),(5,7)]=>[4,6,7,3,8,2,5,1]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,7),(2,6),(3,4),(5,8)]=>[4,6,7,3,8,2,1,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,6),(2,7),(3,4),(5,8)]=>[4,6,7,3,8,1,2,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,5),(2,7),(3,4),(6,8)]=>[4,5,7,3,1,8,2,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,4),(2,7),(3,5),(6,8)]=>[4,5,7,1,3,8,2,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,3),(2,7),(4,5),(6,8)]=>[3,5,1,7,4,8,2,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [(1,2),(3,7),(4,5),(6,8)]=>[2,1,5,7,4,8,3,6]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2},{3,8},{4,5},{6,7}} [(1,2),(3,8),(4,5),(6,7)]=>[2,1,5,7,4,8,6,3]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2},{3,8},{4,5},{6,7}} [(1,3),(2,8),(4,5),(6,7)]=>[3,5,1,7,4,8,6,2]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [(1,4),(2,8),(3,5),(6,7)]=>[4,5,7,1,3,8,6,2]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,5),(2,8),(3,4),(6,7)]=>[4,5,7,3,1,8,6,2]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,6),(2,8),(3,4),(5,7)]=>[4,6,7,3,8,1,5,2]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,7),(2,8),(3,4),(5,6)]=>[4,6,7,3,8,5,1,2]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,8),(2,7),(3,4),(5,6)]=>[4,6,7,3,8,5,2,1]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,8),(2,7),(3,5),(4,6)]=>[5,6,7,8,3,4,2,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,7),(2,8),(3,5),(4,6)]=>[5,6,7,8,3,4,1,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,6),(2,8),(3,5),(4,7)]=>[5,6,7,8,3,1,4,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,5),(2,8),(3,6),(4,7)]=>[5,6,7,8,1,3,4,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,4),(2,8),(3,6),(5,7)]=>[4,6,7,1,8,3,5,2]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,3),(2,8),(4,6),(5,7)]=>[3,6,1,7,8,4,5,2]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,2),(3,8),(4,6),(5,7)]=>[2,1,6,7,8,4,5,3]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,8},{4,7},{5,6}} [(1,2),(3,7),(4,6),(5,8)]=>[2,1,6,7,8,4,3,5]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,8},{4,7},{5,6}} [(1,3),(2,7),(4,6),(5,8)]=>[3,6,1,7,8,4,2,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,4),(2,7),(3,6),(5,8)]=>[4,6,7,1,8,3,2,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,5),(2,7),(3,6),(4,8)]=>[5,6,7,8,1,3,2,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,6),(2,7),(3,5),(4,8)]=>[5,6,7,8,3,1,2,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,7),(2,6),(3,5),(4,8)]=>[5,6,7,8,3,2,1,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,8),(2,6),(3,5),(4,7)]=>[5,6,7,8,3,2,4,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,8),(2,5),(3,6),(4,7)]=>[5,6,7,8,2,3,4,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,7),(2,5),(3,6),(4,8)]=>[5,6,7,8,2,3,1,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,6),(2,5),(3,7),(4,8)]=>[5,6,7,8,2,1,3,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,8},{4,7},{5,6}} [(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2},{3,8},{4,5},{6,7}} [(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,5),(2,4),(3,7),(6,8)]=>[4,5,7,2,1,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,6),(2,4),(3,7),(5,8)]=>[4,6,7,2,8,1,3,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,7),(2,4),(3,6),(5,8)]=>[4,6,7,2,8,3,1,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,8),(2,4),(3,6),(5,7)]=>[4,6,7,2,8,3,5,1]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,8),(2,3),(4,6),(5,7)]=>[3,6,2,7,8,4,5,1]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,7),(2,3),(4,6),(5,8)]=>[3,6,2,7,8,4,1,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,6),(2,3),(4,7),(5,8)]=>[3,6,2,7,8,1,4,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,5),(2,3),(4,7),(6,8)]=>[3,5,2,7,1,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [(1,4),(2,3),(5,7),(6,8)]=>[3,4,2,1,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4},{2,3},{5,8},{6,7}} [(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4},{2,3},{5,8},{6,7}} [(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}}=>{{1,2},{3,4},{5,8},{6,7}} [(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,7,8,6,5]=>{{1,2},{3,4},{5,7},{6,8}}=>{{1,2},{3,4},{5,8},{6,7}} [(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,7,8,6,5]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4},{2,3},{5,8},{6,7}} [(1,4),(2,3),(5,8),(6,7)]=>[3,4,2,1,7,8,6,5]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4},{2,3},{5,8},{6,7}} [(1,5),(2,3),(4,8),(6,7)]=>[3,5,2,7,1,8,6,4]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [(1,6),(2,3),(4,8),(5,7)]=>[3,6,2,7,8,1,5,4]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,7),(2,3),(4,8),(5,6)]=>[3,6,2,7,8,5,1,4]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,8),(2,3),(4,7),(5,6)]=>[3,6,2,7,8,5,4,1]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,8),(2,4),(3,7),(5,6)]=>[4,6,7,2,8,5,3,1]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,7),(2,4),(3,8),(5,6)]=>[4,6,7,2,8,5,1,3]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,6),(2,4),(3,8),(5,7)]=>[4,6,7,2,8,1,5,3]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,5),(2,4),(3,8),(6,7)]=>[4,5,7,2,1,8,6,3]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,4),(2,5),(3,8),(6,7)]=>[4,5,7,1,2,8,6,3]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4},{6,7}} [(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,7,2,8,6,4]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3},{4,5},{6,7}} [(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,7,3,8,6,4]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2},{3,8},{4,5},{6,7}} [(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,7,8,3,5,4]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,8},{4,7},{5,6}} [(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,7,8,2,5,4]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,4),(2,6),(3,8),(5,7)]=>[4,6,7,1,8,2,5,3]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,5),(2,6),(3,8),(4,7)]=>[5,6,7,8,1,2,4,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,6),(2,5),(3,8),(4,7)]=>[5,6,7,8,2,1,4,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,7),(2,5),(3,8),(4,6)]=>[5,6,7,8,2,4,1,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,8),(2,5),(3,7),(4,6)]=>[5,6,7,8,2,4,3,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,8),(2,6),(3,7),(4,5)]=>[5,6,7,8,4,2,3,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,7),(2,6),(3,8),(4,5)]=>[5,6,7,8,4,2,1,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,6),(2,7),(3,8),(4,5)]=>[5,6,7,8,4,1,2,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,5),(2,7),(3,8),(4,6)]=>[5,6,7,8,1,4,2,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,4),(2,7),(3,8),(5,6)]=>[4,6,7,1,8,5,2,3]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,3),(2,7),(4,8),(5,6)]=>[3,6,1,7,8,5,2,4]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,2),(3,7),(4,8),(5,6)]=>[2,1,6,7,8,5,3,4]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,8},{4,7},{5,6}} [(1,2),(3,8),(4,7),(5,6)]=>[2,1,6,7,8,5,4,3]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2},{3,8},{4,7},{5,6}} [(1,3),(2,8),(4,7),(5,6)]=>[3,6,1,7,8,5,4,2]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3},{4,7},{5,6}} [(1,4),(2,8),(3,7),(5,6)]=>[4,6,7,1,8,5,3,2]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4},{5,6}} [(1,5),(2,8),(3,7),(4,6)]=>[5,6,7,8,1,4,3,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,6),(2,8),(3,7),(4,5)]=>[5,6,7,8,4,1,3,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,7),(2,8),(3,6),(4,5)]=>[5,6,7,8,4,3,1,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,8),(2,7),(3,6),(4,5)]=>[5,6,7,8,4,3,2,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}} [(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2},{3,4},{5,6},{7,8},{9,10}} [(1,10),(2,9),(3,8),(4,7),(5,6)]=>[6,7,8,9,10,5,4,3,2,1]=>{{1,6},{2,7},{3,8},{4,9},{5,10}}=>{{1,10},{2,9},{3,8},{4,7},{5,6}} [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
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 $i\leq\pi(i)$.
Map
Chen Deng Du Stanley Yan
Description
A map that swaps the crossing number and the nesting number of a set partition.