Identifier
Values
[1] => [1,0,1,0] => [1,1,0,1,0,0] => 3
[2] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 3
[1,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 3
[3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 4
[2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 4
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 3
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 4
[3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 3
[] => [] => [1,0] => 1
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Description
The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path.
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.