Identifier
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [2,3,1] => [3,2,1] => 1
[2,1,3] => [1,3,2] => [2,3,1] => [3,2,1] => 1
[2,3,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [2,3,4,1] => [4,2,3,1] => 1
[1,3,2,4] => [1,3,2,4] => [2,3,1,4] => [3,2,1,4] => 2
[1,3,4,2] => [1,3,4,2] => [2,4,1,3] => [3,4,1,2] => 2
[1,4,2,3] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[1,4,3,2] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[2,1,3,4] => [1,3,4,2] => [2,4,1,3] => [3,4,1,2] => 2
[2,1,4,3] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[2,3,1,4] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [2,3,1,4] => [3,2,1,4] => 2
[2,4,3,1] => [1,2,4,3] => [2,3,4,1] => [4,2,3,1] => 1
[3,1,2,4] => [1,2,4,3] => [2,3,4,1] => [4,2,3,1] => 1
[3,1,4,2] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[3,2,1,4] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1
[3,2,4,1] => [1,2,4,3] => [2,3,4,1] => [4,2,3,1] => 1
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [2,3,1,4] => [3,2,1,4] => 2
[4,2,1,3] => [1,3,2,4] => [2,3,1,4] => [3,2,1,4] => 2
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => [5,2,3,4,1] => 1
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => [4,2,5,1,3] => 2
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[1,2,5,4,3] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [3,4,2,5,1] => [5,3,2,4,1] => 1
[1,3,4,2,5] => [1,3,4,2,5] => [2,4,1,3,5] => [3,4,1,2,5] => 2
[1,3,4,5,2] => [1,3,4,5,2] => [2,5,1,3,4] => [3,5,1,4,2] => 2
[1,3,5,2,4] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 2
[1,3,5,4,2] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 2
[1,4,2,3,5] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[1,4,2,5,3] => [1,4,2,5,3] => [3,4,5,1,2] => [5,4,3,2,1] => 2
[1,4,3,2,5] => [1,4,2,5,3] => [3,4,5,1,2] => [5,4,3,2,1] => 2
[1,4,3,5,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[1,4,5,2,3] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 2
[1,4,5,3,2] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 2
[1,5,2,3,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[1,5,2,4,3] => [1,5,2,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => 1
[1,5,3,2,4] => [1,5,2,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => 1
[1,5,3,4,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[1,5,4,2,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[1,5,4,3,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[2,1,3,4,5] => [1,3,4,5,2] => [2,5,1,3,4] => [3,5,1,4,2] => 2
[2,1,3,5,4] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 2
[2,1,4,3,5] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[2,1,4,5,3] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 2
[2,1,5,3,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[2,1,5,4,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[2,3,1,4,5] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 2
[2,3,1,5,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[2,3,4,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,3,5,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,5,1] => [5,2,3,4,1] => 1
[2,4,1,3,5] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 2
[2,4,1,5,3] => [1,5,2,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => 1
[2,4,3,1,5] => [1,5,2,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => 1
[2,4,3,5,1] => [1,2,4,3,5] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[2,4,5,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[2,4,5,3,1] => [1,2,4,5,3] => [2,3,5,1,4] => [4,2,5,1,3] => 2
[2,5,1,3,4] => [1,3,4,2,5] => [2,4,1,3,5] => [3,4,1,2,5] => 2
[2,5,1,4,3] => [1,4,2,5,3] => [3,4,5,1,2] => [5,4,3,2,1] => 2
[2,5,3,1,4] => [1,4,2,5,3] => [3,4,5,1,2] => [5,4,3,2,1] => 2
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[2,5,4,1,3] => [1,3,2,5,4] => [3,4,2,5,1] => [5,3,2,4,1] => 1
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[3,1,2,4,5] => [1,2,4,5,3] => [2,3,5,1,4] => [4,2,5,1,3] => 2
[3,1,2,5,4] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[3,1,4,2,5] => [1,4,2,5,3] => [3,4,5,1,2] => [5,4,3,2,1] => 2
[3,1,4,5,2] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 2
[3,1,5,2,4] => [1,5,2,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => 1
[3,1,5,4,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[3,2,1,4,5] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => 2
[3,2,1,5,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[3,2,4,1,5] => [1,5,2,4,3] => [3,2,5,4,1] => [5,2,4,3,1] => 1
[3,2,4,5,1] => [1,2,4,5,3] => [2,3,5,1,4] => [4,2,5,1,3] => 2
[3,2,5,1,4] => [1,4,2,5,3] => [3,4,5,1,2] => [5,4,3,2,1] => 2
[3,2,5,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[3,4,1,2,5] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[3,4,1,5,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[3,4,2,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[3,4,2,5,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[3,4,5,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,4,5,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,5,1,2,4] => [1,2,4,3,5] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[3,5,1,4,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[3,5,2,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
>>> Load all 152 entries. <<<
[3,5,2,4,1] => [1,2,4,3,5] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[3,5,4,1,2] => [1,2,3,5,4] => [2,3,4,5,1] => [5,2,3,4,1] => 1
[3,5,4,2,1] => [1,2,3,5,4] => [2,3,4,5,1] => [5,2,3,4,1] => 1
[4,1,2,3,5] => [1,2,3,5,4] => [2,3,4,5,1] => [5,2,3,4,1] => 1
[4,1,2,5,3] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[4,1,3,2,5] => [1,3,2,5,4] => [3,4,2,5,1] => [5,3,2,4,1] => 1
[4,1,3,5,2] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 2
[4,1,5,2,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[4,1,5,3,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[4,2,1,3,5] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => 2
[4,2,1,5,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[4,2,3,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[4,2,3,5,1] => [1,2,3,5,4] => [2,3,4,5,1] => [5,2,3,4,1] => 1
[4,2,5,1,3] => [1,3,2,5,4] => [3,4,2,5,1] => [5,3,2,4,1] => 1
[4,2,5,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[4,3,1,2,5] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[4,3,1,5,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[4,3,2,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 1
[4,3,2,5,1] => [1,2,5,3,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[4,3,5,1,2] => [1,2,3,5,4] => [2,3,4,5,1] => [5,2,3,4,1] => 1
[4,3,5,2,1] => [1,2,3,5,4] => [2,3,4,5,1] => [5,2,3,4,1] => 1
[4,5,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,1,3,2] => [1,3,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[4,5,2,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[4,5,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,1,2,3,4] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,1,2,4,3] => [1,2,4,3,5] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[5,1,3,2,4] => [1,3,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[5,1,3,4,2] => [1,3,4,2,5] => [2,4,1,3,5] => [3,4,1,2,5] => 2
[5,1,4,2,3] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[5,1,4,3,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[5,2,1,3,4] => [1,3,4,2,5] => [2,4,1,3,5] => [3,4,1,2,5] => 2
[5,2,1,4,3] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[5,2,3,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[5,2,3,4,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,2,4,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[5,2,4,3,1] => [1,2,4,3,5] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[5,3,1,2,4] => [1,2,4,3,5] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[5,3,1,4,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[5,3,2,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 1
[5,3,2,4,1] => [1,2,4,3,5] => [2,3,4,1,5] => [4,2,3,1,5] => 2
[5,3,4,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,3,4,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,1,3,2] => [1,3,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[5,4,2,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[5,4,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,2,1] => [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
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searching the database for statistics with the same generating function
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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
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.