Identifier
Values
=>
Cc0012;cc-rep-0
[(1,2)]=>[2,1]=>0 [(1,2),(3,4)]=>[2,1,4,3]=>2 [(1,3),(2,4)]=>[3,4,1,2]=>0 [(1,4),(2,3)]=>[3,4,2,1]=>1 [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>6 [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>4 [(1,4),(2,3),(5,6)]=>[3,4,2,1,6,5]=>5 [(1,5),(2,3),(4,6)]=>[3,5,2,6,1,4]=>3 [(1,6),(2,3),(4,5)]=>[3,5,2,6,4,1]=>4 [(1,6),(2,4),(3,5)]=>[4,5,6,2,3,1]=>2 [(1,5),(2,4),(3,6)]=>[4,5,6,2,1,3]=>1 [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>0 [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>2 [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>4 [(1,2),(3,6),(4,5)]=>[2,1,5,6,4,3]=>5 [(1,3),(2,6),(4,5)]=>[3,5,1,6,4,2]=>3 [(1,4),(2,6),(3,5)]=>[4,5,6,1,3,2]=>1 [(1,5),(2,6),(3,4)]=>[4,5,6,3,1,2]=>2 [(1,6),(2,5),(3,4)]=>[4,5,6,3,2,1]=>3
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Description
The number of alignments in the permutation.
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.