A cluster theory approach from mutation invariants to Diophantine equations

2025/01/16 by Zhichao Chen, Chen, Zhichao, Zixu Li +1 · 1 citation
Computer Science · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2501.09435

openalex publication_date 2025/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we define and classify the sign-equivalent exchange matrices. We give a Diophantine explanation for the differences between rank 2 cluster algebras of finite type and affine type based on \citeCL24. We classify the positive integer points of the Markov mutation invariant and its variant. As an application, several classes of Diophantine equations with cluster algebraic structures are exhibited.

Cited by

• Generalized discrete Markov spectra

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• The approach of cluster symmetry to Diophantine equations
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