Identifier
Values
{{1,2}} => [2,1] => [1,2] => 0
{{1},{2}} => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [1,2,3] => 0
{{1,2},{3}} => [2,1,3] => [1,3,2] => 1
{{1,3},{2}} => [3,2,1] => [1,2,3] => 0
{{1},{2,3}} => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => [1,2,3,4] => 0
{{1,2,3},{4}} => [2,3,1,4] => [1,4,2,3] => 2
{{1,2,4},{3}} => [2,4,3,1] => [1,2,4,3] => 1
{{1,2},{3,4}} => [2,1,4,3] => [1,4,2,3] => 2
{{1,2},{3},{4}} => [2,1,3,4] => [1,3,4,2] => 2
{{1,3,4},{2}} => [3,2,4,1] => [1,2,4,3] => 1
{{1,3},{2,4}} => [3,4,1,2] => [1,2,3,4] => 0
{{1,3},{2},{4}} => [3,2,1,4] => [1,4,2,3] => 2
{{1,4},{2,3}} => [4,3,2,1] => [1,2,3,4] => 0
{{1},{2,3,4}} => [1,3,4,2] => [1,3,4,2] => 2
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [1,2,3,4] => 0
{{1},{2,4},{3}} => [1,4,3,2] => [1,4,2,3] => 2
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,5,2,3,4] => 2
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,2,3,5,4] => 1
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,5,2,3,4] => 2
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,4,5,2,3] => 2
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,2,4,3,5] => 1
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,3,2,4,5] => 1
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,5,2,4,3] => 2
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,2,5,3,4] => 2
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,4,5,2,3] => 2
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,4,2,3,5] => 2
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,2,5,3,4] => 2
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,5,2,3,4] => 2
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,3,5,2,4] => 2
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,3,4,5,2] => 2
{{1,3,4,5},{2}} => [3,2,4,5,1] => [1,2,4,5,3] => 2
{{1,3,4},{2,5}} => [3,5,4,1,2] => [1,2,3,5,4] => 1
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [1,5,2,4,3] => 2
{{1,3,5},{2,4}} => [3,4,5,2,1] => [1,2,3,4,5] => 0
{{1,3},{2,4,5}} => [3,4,1,5,2] => [1,5,2,3,4] => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [1,2,5,3,4] => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [1,2,5,3,4] => 2
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [1,4,2,3,5] => 2
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [1,5,2,3,4] => 2
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [1,4,5,2,3] => 2
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,2,5,3,4] => 2
{{1,4},{2,3,5}} => [4,3,5,1,2] => [1,2,3,5,4] => 1
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [1,5,2,3,4] => 2
{{1,5},{2,3,4}} => [5,3,4,2,1] => [1,2,3,4,5] => 0
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,3,4,5,2] => 2
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,3,4,2,5] => 2
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [1,2,4,3,5] => 1
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,3,5,2,4] => 2
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => 1
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,2,3,5,4] => 1
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [1,2,3,4,5] => 0
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [1,3,2,5,4] => 1
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [1,5,2,3,4] => 2
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [1,2,3,4,5] => 0
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,4,2,3,5] => 2
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,4,5,2,3] => 2
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,4,2,5,3] => 2
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [1,2,4,3,5] => 1
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,5,2,3,4] => 2
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,4,5,3] => 2
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [1,2,3,4,5] => 0
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,5,2,3,4] => 2
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,5,3,4] => 2
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => 1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => 0
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
click to show known generating functions       
Description
The maximal modular displacement of a permutation.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.