Identifier
Values
[.,.] => [1] => [1] => [1] => 0
[.,[.,.]] => [2,1] => [1,2] => [1,2] => 0
[[.,.],.] => [1,2] => [2,1] => [2,1] => 0
[.,[.,[.,.]]] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[.,[[.,.],.]] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[[.,.],[.,.]] => [1,3,2] => [3,2,1] => [3,2,1] => 0
[[.,[.,.]],.] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[[[.,.],.],.] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [3,2,1,4] => [3,2,1,4] => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,1,2,4] => [3,1,2,4] => 0
[.,[[.,.],[.,.]]] => [2,4,3,1] => [1,3,2,4] => [1,3,2,4] => 0
[.,[[.,[.,.]],.]] => [3,2,4,1] => [2,1,3,4] => [2,1,3,4] => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[[.,.],[.,[.,.]]] => [1,4,3,2] => [4,3,2,1] => [4,3,2,1] => 0
[[.,.],[[.,.],.]] => [1,3,4,2] => [4,2,3,1] => [4,2,3,1] => 0
[[.,[.,.]],[.,.]] => [2,1,4,3] => [1,4,3,2] => [1,4,3,2] => 0
[[[.,.],.],[.,.]] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => 0
[[.,[.,[.,.]]],.] => [3,2,1,4] => [2,1,4,3] => [2,1,4,3] => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => [1,2,4,3] => [1,2,4,3] => 0
[[[.,.],[.,.]],.] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => 0
[[[.,[.,.]],.],.] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => 0
[[[[.,.],.],.],.] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 0
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 0
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [1,5,3,4,2] => [1,5,3,4,2] => 0
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 0
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 0
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [1,2,4,5,3] => [1,2,4,5,3] => 0
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 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
Description
The number of positive entries followed by a negative entry in a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, this is the number of positive entries followed by a negative entry in $\pi(-n),\dots,\pi(-1),\pi(1),\dots,\pi(n)$.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.