Identifier
Values
[1] => [1] => [1,0] => 2
[1,1] => [1,1] => [1,0,1,0] => 3
[1,2] => [1,2] => [1,0,1,1,0,0] => 4
[2,1] => [2,1] => [1,1,0,0,1,0] => 4
[1,1,1] => [1,1,1] => [1,0,1,0,1,0] => 4
[1,1,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 5
[1,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 5
[2,1,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 5
[1,1,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 6
[1,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 6
[3,1,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 6
[1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 6
[2,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 6
[2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 6
[1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,3,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 7
[2,1,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 7
[2,3,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[3,1,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 7
[3,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,1,1,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 5
[1,1,1,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 6
[1,1,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 6
[1,2,1,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 6
[2,1,1,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,3] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,1,3,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 7
[1,3,1,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 7
[3,1,1,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,1,4,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 8
[4,1,1,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 8
[1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,2,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 7
[1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 7
[2,1,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 7
[2,1,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 7
[2,2,1,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 7
[1,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 8
[1,1,3,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[1,2,1,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,2,3,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 8
[1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 8
[1,3,2,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 8
[2,1,1,3] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 8
[2,1,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 8
[2,3,1,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 8
[3,1,1,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 8
[3,1,2,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 8
[3,2,1,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 8
[1,2,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 8
[2,1,2,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8
[2,2,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 8
[2,2,2,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,1,2,1,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,2,1,1,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 7
[2,1,1,1,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,3] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 8
[1,1,1,3,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,3,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 8
[1,3,1,1,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 8
[3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,2,2] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,1,2,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,2,1,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,2,2,1,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 8
[2,1,1,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 8
[2,1,1,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 8
[2,1,2,1,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 8
[2,2,1,1,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,1,1,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,1,1,2,1,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,1,2,1,1,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,2,1,1,1,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 8
[2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
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Description
Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path.
Map
to composition
Description
Return the parking function interpreted as an integer composition.
Map
bounce path
Description
The bounce path determined by an integer composition.