A short proof of the finiteness of Dynkin friezes

2023/12/18 by Greg Muller, Muller, Greg · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2312.11394

openalex publication_date 2023/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a short and elementary proof that every Dynkin diagram admits finitely many (positive integral) friezes. This was originally proven by Gunawan-Muller using the geometry of cluster algebras. The proof here provides an explicit (albeit inefficient) bound on values.

Cited by

• Frieze patterns in representation theory

Related

• Counting friezes in type D_n
• A positive Siegel theorem: Dynkin friezes and positive Mordell-Schinzel
• Non-zero integral friezes
• Linearly recursive sequences and Dynkin diagrams
• Superunitary regions of cluster algebras