Testing Cayley graph Densities (version longue)
Résumé
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: Given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m-generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2m. We test amenable and non-amenable groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson's group F. The sign means that we would like you to check our changes here. ♠
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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