Identifier
Values
[1] => [1] => [1,0] => [2,1] => 1
[2] => [1,1] => [1,1,0,0] => [2,3,1] => 1
[1,1] => [2] => [1,0,1,0] => [3,1,2] => 1
[3] => [3] => [1,0,1,0,1,0] => [4,1,2,3] => 1
[2,1] => [1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => 1
[1,1,1] => [2,1] => [1,0,1,1,0,0] => [3,1,4,2] => 1
[4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 1
[3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 1
[2,2] => [4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 1
[2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
[1,1,1,1] => [2,2] => [1,1,1,0,0,0] => [2,3,4,1] => 1
[3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 1
[1,1,1,1,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
[6] => [3,3] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 1
[1,1,1,1,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 1
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Description
The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$.
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.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.