Identifier
Values
[1,0] => 10 => [1,1] => [1,0,1,0] => 2
[1,0,1,0] => 1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0] => 1100 => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0] => 101010 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0] => 101100 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0] => 110010 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0] => 110100 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0] => 111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
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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.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.