Identifier
Values
[(1,2)] => [2,1] => [1,2] => 0
[(1,2),(3,4)] => [2,1,4,3] => [3,4,1,2] => 2
[(1,3),(2,4)] => [3,4,1,2] => [2,1,4,3] => 3
[(1,4),(2,3)] => [3,4,2,1] => [1,2,4,3] => 3
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 4
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [5,6,2,1,4,3] => 5
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [5,6,1,2,4,3] => 5
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [4,1,6,2,5,3] => 5
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [1,4,6,2,5,3] => 5
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [1,3,2,6,5,4] => 5
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [3,1,2,6,5,4] => 5
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => 5
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => 5
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [4,3,6,5,1,2] => 4
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [3,4,6,5,1,2] => 4
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [2,4,6,1,5,3] => 5
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [2,3,1,6,5,4] => 5
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [2,1,3,6,5,4] => 5
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => 5
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Description
The last descent of a permutation.
For a permutation $\pi$ of $\{1,\ldots,n\}$, this is the largest index $0 \leq i < n$ such that $\pi(i) > \pi(i+1)$ where one considers $\pi(0) = n+1$.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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.