Identifier
Values
[2] => [1,1] => [1,1,0,0] => [1,1,1,0,0,0] => 1
[1,1] => [2] => [1,0,1,0] => [1,1,0,1,0,0] => 1
[3] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[2,1] => [1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 1
[4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[2,2] => [4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,1] => [2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[6] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 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 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
Glaisher-Franklin inverse
Description
The Glaisher-Franklin bijection on integer partitions.
This map sends the number of distinct repeated part sizes to the number of distinct even part sizes, see [1, 3.3.1].
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.