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