Identifier
Values
[1,0] => 10 => [1,1] => 2
[1,0,1,0] => 1010 => [1,1,1,1] => 4
[1,1,0,0] => 1100 => [2,2] => 2
[1,0,1,0,1,0] => 101010 => [1,1,1,1,1,1] => 6
[1,0,1,1,0,0] => 101100 => [1,1,2,2] => 3
[1,1,0,0,1,0] => 110010 => [2,2,1,1] => 3
[1,1,0,1,0,0] => 110100 => [2,1,1,2] => 4
[1,1,1,0,0,0] => 111000 => [3,3] => 2
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Description
The global dimension of the corresponding Comp-Nakayama algebra.
We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".
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 $w$.