Identifier
Values
[1] => [1,0,1,0] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 0
[2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => 0
[1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => 0
[3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1
[2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 1
[3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 0
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 0
[3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 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 global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
inverse promotion
Description
The inverse promotion of a Dyck path.
This is the bijection obtained by applying the inverse of Schützenberger's promotion to the corresponding two rowed standard Young tableau.