Log-concavity and unimodality of cluster monomials of type $A_3$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918499088072704 |
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| author | Chen, Zhichao |
| author_facet | Chen, Zhichao |
| contents | The log-concavity of cluster variables of type $A_n$ and cluster monomials of type $A_2$ was established by Chen-Huang-Sun. It is still a conjecture for the cluster monomials of higher rank. In this paper, we prove the log-concavity and unimodality of the cluster monomials of type $A_3$, a substantially more intricate case. Moreover, we refine and extend this conjecture by considering the unimodality and the strongly isomorphism of cluster algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_21496 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log-concavity and unimodality of cluster monomials of type $A_3$ Chen, Zhichao Representation Theory Combinatorics Rings and Algebras 13F60, 05E10, 05A20 The log-concavity of cluster variables of type $A_n$ and cluster monomials of type $A_2$ was established by Chen-Huang-Sun. It is still a conjecture for the cluster monomials of higher rank. In this paper, we prove the log-concavity and unimodality of the cluster monomials of type $A_3$, a substantially more intricate case. Moreover, we refine and extend this conjecture by considering the unimodality and the strongly isomorphism of cluster algebras. |
| title | Log-concavity and unimodality of cluster monomials of type $A_3$ |
| topic | Representation Theory Combinatorics Rings and Algebras 13F60, 05E10, 05A20 |
| url | https://arxiv.org/abs/2601.21496 |