Processing math: 100%

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] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[2,1,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[2,3,1] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,3,2] => [2,3,1] => [1,2,3] => 0
[3,2,1] => [1,3,2] => [2,3,1] => [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] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,3,2,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,3,4,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,4,2,3] => [1,2,4,3] => [2,3,4,1] => [1,2,3,4] => 0
[1,4,3,2] => [1,2,4,3] => [2,3,4,1] => [1,2,3,4] => 0
[2,1,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,1,4,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,3,1,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,1,3] => [1,2,4,3] => [2,3,4,1] => [1,2,3,4] => 0
[2,4,3,1] => [1,2,4,3] => [2,3,4,1] => [1,2,3,4] => 0
[3,1,2,4] => [1,3,2,4] => [2,3,1,4] => [1,2,3,4] => 0
[3,1,4,2] => [1,3,4,2] => [2,4,1,3] => [1,2,4,3] => 0
[3,2,1,4] => [1,3,2,4] => [2,3,1,4] => [1,2,3,4] => 0
[3,2,4,1] => [1,3,4,2] => [2,4,1,3] => [1,2,4,3] => 0
[3,4,1,2] => [1,3,2,4] => [2,3,1,4] => [1,2,3,4] => 0
[3,4,2,1] => [1,3,2,4] => [2,3,1,4] => [1,2,3,4] => 0
[4,1,2,3] => [1,4,3,2] => [3,4,2,1] => [1,3,2,4] => 1
[4,1,3,2] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[4,2,1,3] => [1,4,3,2] => [3,4,2,1] => [1,3,2,4] => 1
[4,2,3,1] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[4,3,1,2] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[4,3,2,1] => [1,4,2,3] => [2,1,4,3] => [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] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,5,3,4] => [1,2,3,5,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,2,5,4,3] => [1,2,3,5,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,3,2,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,3,2,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,3,4,2,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,3,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,3,5,2,4] => [1,2,3,5,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,3,5,4,2] => [1,2,3,5,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,4,2,3,5] => [1,2,4,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[1,4,2,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => 0
[1,4,3,2,5] => [1,2,4,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[1,4,3,5,2] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => 0
[1,4,5,2,3] => [1,2,4,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[1,4,5,3,2] => [1,2,4,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[1,5,2,3,4] => [1,2,5,4,3] => [3,4,5,2,1] => [1,3,5,2,4] => 1
[1,5,2,4,3] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[1,5,3,2,4] => [1,2,5,4,3] => [3,4,5,2,1] => [1,3,5,2,4] => 1
[1,5,3,4,2] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[1,5,4,2,3] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[1,5,4,3,2] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,1,5,3,4] => [1,2,3,5,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[2,1,5,4,3] => [1,2,3,5,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[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] => [1,2,3,5,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[2,4,1,3,5] => [1,2,4,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[2,4,1,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => 0
[2,4,3,1,5] => [1,2,4,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[2,4,3,5,1] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => 0
[2,4,5,1,3] => [1,2,4,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[2,4,5,3,1] => [1,2,4,3,5] => [2,3,4,1,5] => [1,2,3,4,5] => 0
[2,5,1,3,4] => [1,2,5,4,3] => [3,4,5,2,1] => [1,3,5,2,4] => 1
[2,5,1,4,3] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[2,5,3,1,4] => [1,2,5,4,3] => [3,4,5,2,1] => [1,3,5,2,4] => 1
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[2,5,4,1,3] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => 0
[3,1,2,4,5] => [1,3,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[3,1,2,5,4] => [1,3,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[3,1,4,2,5] => [1,3,4,2,5] => [2,4,1,3,5] => [1,2,4,3,5] => 0
[3,1,4,5,2] => [1,3,4,5,2] => [2,5,1,3,4] => [1,2,5,4,3] => 0
[3,1,5,2,4] => [1,3,5,4,2] => [3,5,2,4,1] => [1,3,2,5,4] => 1
[3,1,5,4,2] => [1,3,5,2,4] => [2,1,4,5,3] => [1,2,3,4,5] => 0
[3,2,1,4,5] => [1,3,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[3,2,1,5,4] => [1,3,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[3,2,4,1,5] => [1,3,4,2,5] => [2,4,1,3,5] => [1,2,4,3,5] => 0
[3,2,4,5,1] => [1,3,4,5,2] => [2,5,1,3,4] => [1,2,5,4,3] => 0
[3,2,5,1,4] => [1,3,5,4,2] => [3,5,2,4,1] => [1,3,2,5,4] => 1
[3,2,5,4,1] => [1,3,5,2,4] => [2,1,4,5,3] => [1,2,3,4,5] => 0
[3,4,1,2,5] => [1,3,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[3,4,1,5,2] => [1,3,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[3,4,2,1,5] => [1,3,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[3,4,2,5,1] => [1,3,2,4,5] => [2,3,1,4,5] => [1,2,3,4,5] => 0
[3,4,5,1,2] => [1,3,5,2,4] => [2,1,4,5,3] => [1,2,3,4,5] => 0
[3,4,5,2,1] => [1,3,5,2,4] => [2,1,4,5,3] => [1,2,3,4,5] => 0
[3,5,1,2,4] => [1,3,2,5,4] => [3,4,2,5,1] => [1,3,2,4,5] => 1
[3,5,1,4,2] => [1,3,2,5,4] => [3,4,2,5,1] => [1,3,2,4,5] => 1
[3,5,2,1,4] => [1,3,2,5,4] => [3,4,2,5,1] => [1,3,2,4,5] => 1
>>> Load all 152 entries. <<<
[3,5,2,4,1] => [1,3,2,5,4] => [3,4,2,5,1] => [1,3,2,4,5] => 1
[3,5,4,1,2] => [1,3,4,2,5] => [2,4,1,3,5] => [1,2,4,3,5] => 0
[3,5,4,2,1] => [1,3,4,2,5] => [2,4,1,3,5] => [1,2,4,3,5] => 0
[4,1,2,3,5] => [1,4,3,2,5] => [3,4,2,1,5] => [1,3,2,4,5] => 1
[4,1,2,5,3] => [1,4,5,3,2] => [3,5,4,1,2] => [1,3,4,2,5] => 1
[4,1,3,2,5] => [1,4,2,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[4,1,3,5,2] => [1,4,5,2,3] => [2,1,5,3,4] => [1,2,3,5,4] => 0
[4,1,5,2,3] => [1,4,2,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[4,1,5,3,2] => [1,4,3,5,2] => [3,5,2,1,4] => [1,3,2,5,4] => 1
[4,2,1,3,5] => [1,4,3,2,5] => [3,4,2,1,5] => [1,3,2,4,5] => 1
[4,2,1,5,3] => [1,4,5,3,2] => [3,5,4,1,2] => [1,3,4,2,5] => 1
[4,2,3,1,5] => [1,4,2,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[4,2,3,5,1] => [1,4,5,2,3] => [2,1,5,3,4] => [1,2,3,5,4] => 0
[4,2,5,1,3] => [1,4,2,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[4,2,5,3,1] => [1,4,3,5,2] => [3,5,2,1,4] => [1,3,2,5,4] => 1
[4,3,1,2,5] => [1,4,2,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[4,3,1,5,2] => [1,4,5,2,3] => [2,1,5,3,4] => [1,2,3,5,4] => 0
[4,3,2,1,5] => [1,4,2,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[4,3,2,5,1] => [1,4,5,2,3] => [2,1,5,3,4] => [1,2,3,5,4] => 0
[4,3,5,1,2] => [1,4,2,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[4,3,5,2,1] => [1,4,2,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 0
[4,5,1,2,3] => [1,4,2,5,3] => [3,4,5,1,2] => [1,3,5,2,4] => 1
[4,5,1,3,2] => [1,4,3,2,5] => [3,4,2,1,5] => [1,3,2,4,5] => 1
[4,5,2,1,3] => [1,4,2,5,3] => [3,4,5,1,2] => [1,3,5,2,4] => 1
[4,5,2,3,1] => [1,4,3,2,5] => [3,4,2,1,5] => [1,3,2,4,5] => 1
[4,5,3,1,2] => [1,4,2,5,3] => [3,4,5,1,2] => [1,3,5,2,4] => 1
[4,5,3,2,1] => [1,4,2,5,3] => [3,4,5,1,2] => [1,3,5,2,4] => 1
[5,1,2,3,4] => [1,5,4,3,2] => [4,5,3,2,1] => [1,4,2,5,3] => 2
[5,1,2,4,3] => [1,5,3,2,4] => [3,4,1,5,2] => [1,3,2,4,5] => 1
[5,1,3,2,4] => [1,5,4,2,3] => [3,1,5,4,2] => [1,3,5,2,4] => 1
[5,1,3,4,2] => [1,5,2,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[5,1,4,2,3] => [1,5,3,4,2] => [3,5,1,4,2] => [1,3,2,5,4] => 1
[5,1,4,3,2] => [1,5,2,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[5,2,1,3,4] => [1,5,4,3,2] => [4,5,3,2,1] => [1,4,2,5,3] => 2
[5,2,1,4,3] => [1,5,3,2,4] => [3,4,1,5,2] => [1,3,2,4,5] => 1
[5,2,3,1,4] => [1,5,4,2,3] => [3,1,5,4,2] => [1,3,5,2,4] => 1
[5,2,3,4,1] => [1,5,2,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[5,2,4,1,3] => [1,5,3,4,2] => [3,5,1,4,2] => [1,3,2,5,4] => 1
[5,2,4,3,1] => [1,5,2,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[5,3,1,2,4] => [1,5,4,2,3] => [3,1,5,4,2] => [1,3,5,2,4] => 1
[5,3,1,4,2] => [1,5,2,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[5,3,2,1,4] => [1,5,4,2,3] => [3,1,5,4,2] => [1,3,5,2,4] => 1
[5,3,2,4,1] => [1,5,2,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[5,3,4,1,2] => [1,5,2,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[5,3,4,2,1] => [1,5,2,3,4] => [2,1,3,5,4] => [1,2,3,4,5] => 0
[5,4,1,2,3] => [1,5,3,2,4] => [3,4,1,5,2] => [1,3,2,4,5] => 1
[5,4,1,3,2] => [1,5,2,4,3] => [3,2,5,4,1] => [1,3,5,2,4] => 1
[5,4,2,1,3] => [1,5,3,2,4] => [3,4,1,5,2] => [1,3,2,4,5] => 1
[5,4,2,3,1] => [1,5,2,4,3] => [3,2,5,4,1] => [1,3,5,2,4] => 1
[5,4,3,1,2] => [1,5,2,4,3] => [3,2,5,4,1] => [1,3,5,2,4] => 1
[5,4,3,2,1] => [1,5,2,4,3] => [3,2,5,4,1] => [1,3,5,2,4] => 1
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 number of inversions of the second entry of a permutation.
This is, for a permutation π of length n,
#{2<knπ(2)>π(k)}.
The number of inversions of the first entry is St000054The first entry of the permutation. and the number of inversions of the third entry is St001556The number of inversions of the third entry of a permutation.. The sequence of inversions of all the entries define the Lehmer code of a permutation.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
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.