Identifier
Values
[1] => [1,0,1,0] => [1,0,1,0] => 2
[2] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 2
[1,1] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 2
[3] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => 3
[2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 2
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 2
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[3,2] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 3
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 2
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 3
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 3
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 3
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 2
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 2
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 2
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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
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.