Identifier
Values
[1] => [1,0] => [2,1] => [1,2] => 1
[1,1] => [1,0,1,0] => [3,1,2] => [1,3,2] => 1
[2] => [1,1,0,0] => [2,3,1] => [3,1,2] => 1
[1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => [1,3,4,2] => 1
[1,2] => [1,0,1,1,0,0] => [3,1,4,2] => [4,2,1,3] => 1
[2,1] => [1,1,0,0,1,0] => [2,4,1,3] => [3,1,4,2] => 1
[3] => [1,1,1,0,0,0] => [2,3,4,1] => [3,4,1,2] => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [1,3,4,5,2] => 1
[1,1,2] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5,2,3,1,4] => 1
[1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [4,2,1,5,3] => 1
[1,3] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [4,2,5,1,3] => 1
[2,1,1] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [3,1,4,5,2] => 1
[2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [3,5,2,1,4] => 1
[3,1] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [3,4,1,5,2] => 1
[4] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [3,4,5,1,2] => 1
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [1,3,4,5,6,2] => 1
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [6,2,3,4,1,5] => 1
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [5,2,3,1,6,4] => 1
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [5,2,3,6,1,4] => 1
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [4,2,1,5,6,3] => 1
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [4,2,6,3,1,5] => 1
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [4,2,5,1,6,3] => 1
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [4,2,5,6,1,3] => 1
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => 1
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,6,2,4,1,5] => 2
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [3,5,2,1,6,4] => 1
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [3,5,2,6,1,4] => 1
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [3,4,1,5,6,2] => 1
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [3,4,6,2,1,5] => 1
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [3,4,5,1,6,2] => 1
[5] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [3,4,5,6,1,2] => 1
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [1,3,4,5,6,7,2] => 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
Description
The neighbouring number of a permutation.
For a permutation $\pi$, this is
$$\min \big(\big\{|\pi(k)-\pi(k+1)|:k\in\{1,\ldots,n-1\}\big\}\cup \big\{|\pi(1) - \pi(n)|\big\}\big).$$
Map
Lehmer code rotation
Description
Sends a permutation $\pi$ to the unique permutation $\tau$ (of the same length) such that every entry in the Lehmer code of $\tau$ is cyclically one larger than the Lehmer code of $\pi$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.