Identifier
Values
{{1}} => [1] => [1,0] => 1
{{1,2}} => [2] => [1,1,0,0] => 2
{{1},{2}} => [1,1] => [1,0,1,0] => 2
{{1,2,3}} => [3] => [1,1,1,0,0,0] => 3
{{1,2},{3}} => [2,1] => [1,1,0,0,1,0] => 2
{{1,3},{2}} => [2,1] => [1,1,0,0,1,0] => 2
{{1},{2,3}} => [1,2] => [1,0,1,1,0,0] => 2
{{1},{2},{3}} => [1,1,1] => [1,0,1,0,1,0] => 2
{{1,2,3,4}} => [4] => [1,1,1,1,0,0,0,0] => 4
{{1,2,3},{4}} => [3,1] => [1,1,1,0,0,0,1,0] => 3
{{1,2,4},{3}} => [3,1] => [1,1,1,0,0,0,1,0] => 3
{{1,2},{3,4}} => [2,2] => [1,1,0,0,1,1,0,0] => 2
{{1,2},{3},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
{{1,3,4},{2}} => [3,1] => [1,1,1,0,0,0,1,0] => 3
{{1,3},{2,4}} => [2,2] => [1,1,0,0,1,1,0,0] => 2
{{1,3},{2},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
{{1,4},{2,3}} => [2,2] => [1,1,0,0,1,1,0,0] => 2
{{1},{2,3,4}} => [1,3] => [1,0,1,1,1,0,0,0] => 3
{{1},{2,3},{4}} => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
{{1,4},{2},{3}} => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
{{1},{2,4},{3}} => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
{{1},{2},{3,4}} => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
{{1},{2},{3},{4}} => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
{{1,2,3,4,5}} => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
{{1,2,3,4},{5}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
{{1,2,3,5},{4}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
{{1,2,3},{4,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
{{1,2,3},{4},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
{{1,2,4,5},{3}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
{{1,2,4},{3,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
{{1,2,4},{3},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
{{1,2,5},{3,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
{{1,2},{3,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
{{1,2},{3,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
{{1,2,5},{3},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
{{1,2},{3,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
{{1,2},{3},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
{{1,2},{3},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
{{1,3,4,5},{2}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
{{1,3,4},{2,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
{{1,3,4},{2},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
{{1,3,5},{2,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
{{1,3},{2,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
{{1,3},{2,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
{{1,3,5},{2},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
{{1,3},{2,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
{{1,3},{2},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
{{1,3},{2},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
{{1,4,5},{2,3}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
{{1,4},{2,3,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
{{1,4},{2,3},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
{{1,5},{2,3,4}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
{{1},{2,3,4,5}} => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
{{1},{2,3,4},{5}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
{{1,5},{2,3},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
{{1},{2,3,5},{4}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
{{1},{2,3},{4,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
{{1},{2,3},{4},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
{{1,4,5},{2},{3}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
{{1,4},{2,5},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
{{1,4},{2},{3,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
{{1,4},{2},{3},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
{{1,5},{2,4},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
{{1},{2,4,5},{3}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
{{1},{2,4},{3,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
{{1},{2,4},{3},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
{{1,5},{2},{3,4}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
{{1},{2,5},{3,4}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
{{1},{2},{3,4,5}} => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
{{1},{2},{3,4},{5}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
{{1,5},{2},{3},{4}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
{{1},{2,5},{3},{4}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
{{1},{2},{3,5},{4}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
{{1},{2},{3},{4,5}} => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [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
bounce path
Description
The bounce path determined by an integer composition.
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.