A cluster theory approach from mutation invariants to Diophantine equations
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909457770872832 |
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| author | Chen, Zhichao Li, Zixu |
| author_facet | Chen, Zhichao Li, Zixu |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A cluster theory approach from mutation invariants to Diophantine equations Chen, Zhichao Li, Zixu Number Theory Combinatorics Rings and Algebras Representation Theory 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. |
| title | A cluster theory approach from mutation invariants to Diophantine equations |
| topic | Number Theory Combinatorics Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2501.09435 |