Identifier
-
Mp00230:
Integer partitions
—parallelogram polyomino⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
St001207: Permutations ⟶ ℤ
Values
[1] => [1,0] => [2,1] => [1,2] => 0
[2] => [1,0,1,0] => [3,1,2] => [1,2,3] => 0
[1,1] => [1,1,0,0] => [2,3,1] => [1,2,3] => 0
[3] => [1,0,1,0,1,0] => [4,1,2,3] => [1,2,3,4] => 0
[2,1] => [1,0,1,1,0,0] => [3,1,4,2] => [1,4,2,3] => 2
[1,1,1] => [1,1,0,1,0,0] => [4,3,1,2] => [1,2,3,4] => 0
[2,2] => [1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => 0
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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
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.
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.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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