Identifier
Values
[1] => [1,0] => 1
[1,1] => [1,0,1,0] => 2
[2] => [1,1,0,0] => 1
[1,1,1] => [1,0,1,0,1,0] => 3
[1,2] => [1,0,1,1,0,0] => 2
[2,1] => [1,1,0,0,1,0] => 2
[3] => [1,1,1,0,0,0] => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,2] => [1,0,1,0,1,1,0,0] => 3
[1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,3] => [1,0,1,1,1,0,0,0] => 2
[2,1,1] => [1,1,0,0,1,0,1,0] => 3
[2,2] => [1,1,0,0,1,1,0,0] => 2
[3,1] => [1,1,1,0,0,0,1,0] => 2
[4] => [1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 4
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 3
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 2
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
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Description
The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver.
The $k$-Gorenstein degree is the maximal number $k$ such that the algebra is $k$-Gorenstein. We apply the convention that the value is equal to the global dimension of the algebra in case the $k$-Gorenstein degree is greater than or equal to the global dimension.
Map
bounce path
Description
The bounce path determined by an integer composition.