Identifier
Values
=>
Cc0012;cc-rep-0
[(1,2)]=>[2,1]=>0 [(1,2),(3,4)]=>[2,1,4,3]=>0 [(1,3),(2,4)]=>[3,4,1,2]=>1 [(1,4),(2,3)]=>[4,3,2,1]=>2 [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>0 [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>1 [(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>2 [(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>3 [(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>4 [(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>5 [(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>4 [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>3 [(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]=>1 [(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>2 [(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>3 [(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>4 [(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>5 [(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>6
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Description
The number of invisible inversions of a permutation.
A visible inversion of a permutation $\pi$ is a pair $i < j$ such that $\pi(j) \leq \min(i, \pi(i))$. Thus, an invisible inversion satisfies $\pi(i) > \pi(j) > i$.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.