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
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 $n+1-i$.
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.