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arXiv · 2601.21496

Log-concavity and unimodality of cluster monomials of type $A_3$

Zhichao Chen
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Abstract

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.

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BibTeXRIS

Zhichao Chen. 2026-01-29. Log-concavity and unimodality of cluster monomials of type $A_3$. https://arxiv.org/abs/2601.21496

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