从突变不变量到丢番图方程的簇理论方法
A cluster theory approach from mutation invariants to Diophantine equations
AI总结：
该研究采用簇理论方法，定义分类符号等价交换矩阵，解释有限型与仿射型秩2簇代数差异，分类马尔可夫突变不变量正整数点，展示多类带簇代数结构的丢番图方程。
摘要：
本文定义并分类了符号等价交换矩阵。基于文献\textit{CL24}，我们对有限型与仿射型秩2簇代数之间的差异给出了丢番图解释。我们分类了马尔可夫突变不变量及其变体的正整数点。作为应用，我们展示了几类具有簇代数结构的丢番图方程。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
