From frieze patterns to cluster categories
Matthew Pressland
TL;DR
This paper explores the connection between frieze patterns and modern algebraic structures like cluster algebras and categories, explaining their properties through these advanced theories.
Contribution
It introduces cluster algebras and categories to provide a conceptual framework for understanding frieze patterns, highlighting their integrality and periodicity.
Findings
Cluster algebras explain frieze pattern properties
Categorical perspective clarifies integrality
Theories unify combinatorial and algebraic aspects
Abstract
Motivated by Conway and Coxeter's combinatorial results concerning frieze patterns, we sketch an introduction to the theory of cluster algebras and cluster categories for acyclic quivers. The goal is to show how these more abstract theories provide a conceptual explanation for phenomena concerning friezes, principally integrality and periodicity.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology