Processing math: 100%

Identifier
Values
['A',1] => ([],1) => ([],1) => [1] => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => [1,1,1] => 3
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => [1,2,1] => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [1,1,1,1,1,1] => 6
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [1,1,1,1,1,1] => 6
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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 graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
Laplacian multiplicities
Description
The composition of multiplicities of the Laplacian eigenvalues.
Let λ1>λ2> be the eigenvalues of the Laplacian matrix of a graph on n vertices. Then this map returns the composition a1,,ak of n where ai is the multiplicity of λi.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where αβ if βα is a simple root.