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Bibliographic Details
Main Authors:	Chen, Zhichao, Li, Zixu
Format:	Preprint
Published:	2025
Subjects:	Number Theory Combinatorics Rings and Algebras Representation Theory
Online Access:	https://arxiv.org/abs/2501.09435
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Table of Contents:

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 \cite{CL24}. 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.