Identifier
Values
[(1,2)] => [(1,2)] => [2,1] => [1] => 0
[(1,2),(3,4)] => [(1,2),(3,4)] => [2,1,4,3] => [2,1,3] => 1
[(1,3),(2,4)] => [(1,3),(2,4)] => [3,4,1,2] => [3,1,2] => 1
[(1,4),(2,3)] => [(1,4),(2,3)] => [3,4,2,1] => [3,2,1] => 1
[(1,2),(3,4),(5,6)] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,5] => 1
[(1,3),(2,4),(5,6)] => [(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,5,3,4] => 1
[(1,4),(2,3),(5,6)] => [(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [2,1,5,4,3] => 1
[(1,5),(2,3),(4,6)] => [(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [3,5,1,4,2] => 2
[(1,6),(2,3),(4,5)] => [(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [3,5,2,4,1] => 2
[(1,6),(2,4),(3,5)] => [(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [4,5,2,3,1] => 2
[(1,5),(2,4),(3,6)] => [(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [4,5,1,3,2] => 2
[(1,4),(2,5),(3,6)] => [(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [4,5,1,2,3] => 2
[(1,3),(2,5),(4,6)] => [(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [3,5,1,2,4] => 2
[(1,2),(3,5),(4,6)] => [(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [3,4,1,2,5] => 2
[(1,2),(3,6),(4,5)] => [(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [3,4,2,1,5] => 2
[(1,3),(2,6),(4,5)] => [(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [3,5,2,1,4] => 2
[(1,4),(2,6),(3,5)] => [(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [4,5,2,1,3] => 2
[(1,5),(2,6),(3,4)] => [(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [4,5,3,1,2] => 2
[(1,6),(2,5),(3,4)] => [(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [4,5,3,2,1] => 2
[(1,5),(2,6),(3,7),(4,8)] => [(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [5,6,7,1,2,3,4] => 3
[(1,2),(3,6),(4,7),(5,8)] => [(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [4,5,6,1,2,3,7] => 3
[(1,2),(3,8),(4,7),(5,6)] => [(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [4,5,6,3,2,1,7] => 3
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [6,7,8,9,1,2,3,4,5] => 4
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The Elizalde-Pak rank of a permutation.
This is the largest $k$ such that $\pi(i) > k$ for all $i\leq k$.
According to [1], the length of the longest increasing subsequence in a $321$-avoiding permutation is equidistributed with the rank of a $132$-avoiding 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.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
Map
reverse
Description
The reverse of a perfect matching of $\{1,2,...,n\}$.
This is the perfect matching obtained by replacing $i$ by $n+1-i$.