Identifier
-
Mp00231:
Integer compositions
—bounce path⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001868: Signed permutations ⟶ ℤ
Values
[1] => [1,0] => [2,1] => [2,1] => 0
[1,1] => [1,0,1,0] => [3,1,2] => [3,1,2] => 0
[2] => [1,1,0,0] => [2,3,1] => [2,3,1] => 0
[1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => [4,1,2,3] => 0
[1,2] => [1,0,1,1,0,0] => [3,1,4,2] => [3,1,4,2] => 1
[2,1] => [1,1,0,0,1,0] => [2,4,1,3] => [2,4,1,3] => 0
[3] => [1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => 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 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 $\pi(i) < i < j \leq \pi(j)$.
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
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to signed permutation
Description
The signed permutation with all signs positive.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!