Log-concavity of cluster algebras of type $A_n$
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916447259721728 |
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| author | Chen, Zhichao Huang, Guanhua Sun, Zhe |
| author_facet | Chen, Zhichao Huang, Guanhua Sun, Zhe |
| contents | Okounkov [Oko03] conjectured the log-concavity about the structure constants for many interesting basis from representation theory. For the cluster algebra, Gross, Hacking, Keel, Kontsevich [GHKK18] introduced the atomic theta basis. We prove that the coefficients of the exponents of any cluster variable of type $A_n$ are log-concave. We show that the structure constants for theta basis of type $A_2$ are log-concave. As for larger generality, we conjecture that the log-concavity of the structure constants for theta basis of the cluster algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log-concavity of cluster algebras of type $A_n$ Chen, Zhichao Huang, Guanhua Sun, Zhe Representation Theory Combinatorics Geometric Topology 13F60, 16S99, 16G20, 05E16 Okounkov [Oko03] conjectured the log-concavity about the structure constants for many interesting basis from representation theory. For the cluster algebra, Gross, Hacking, Keel, Kontsevich [GHKK18] introduced the atomic theta basis. We prove that the coefficients of the exponents of any cluster variable of type $A_n$ are log-concave. We show that the structure constants for theta basis of type $A_2$ are log-concave. As for larger generality, we conjecture that the log-concavity of the structure constants for theta basis of the cluster algebra. |
| title | Log-concavity of cluster algebras of type $A_n$ |
| topic | Representation Theory Combinatorics Geometric Topology 13F60, 16S99, 16G20, 05E16 |
| url | https://arxiv.org/abs/2408.03792 |