Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [2,1] => [2,1] => 0
[1,1,0,0] => [1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [2,1,3] => [2,1,3] => [2,1,3] => 1
[1,0,1,1,0,0] => [2,3,1] => [1,3,2] => [1,3,2] => 0
[1,1,0,0,1,0] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[1,1,0,1,0,0] => [1,3,2] => [1,3,2] => [1,3,2] => 0
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [2,4,1,3] => [2,4,1,3] => 0
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,2,4,3] => [1,2,4,3] => 0
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [2,1,4,3] => [2,1,4,3] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,4,1,3] => [2,4,1,3] => 0
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [3,1,2,4] => [3,1,2,4] => 2
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [1,2,4,3] => [1,2,4,3] => 0
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [4,1,2,3] => [4,1,2,3] => 0
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 0
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [1,3,2,5,4] => [1,3,2,5,4] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,1,1,1,1,0,0,0,0,0] => [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 number of alignments of type NE of a signed permutation.
An alignment of type NE of a signed permutation $\pi\in\mathfrak H_n$ is a pair $1 \leq i, j\leq n$ such that $\pi(i) < i < j \leq \pi(j)$.
Map
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
to signed permutation
Description
The signed permutation with all signs positive.