Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics

TL;DR

This paper reviews Coxeter's frieze patterns, highlighting their historical origins and recent connections with cluster algebras through algebraic, geometric, and combinatorial perspectives.

Contribution

It synthesizes Coxeter's original work with recent advances, emphasizing the interdisciplinary approaches to understanding frieze patterns.

Findings

Connections between frieze patterns and cluster algebras

Representation theoretic interpretations of frieze patterns

Geometric and combinatorial frameworks for frieze analysis

Abstract

Frieze patterns of numbers, introduced in the early 70's by Coxeter, are currently attracting much interest due to connections with the recent theory of cluster algebras. The present paper aims to review the original work of Coxeter and the new developments around the notion of frieze, focusing on the representation theoretic, geometric and combinatorial approaches.