Log-concavity and unimodality of cluster monomials of type A3
Abstract
The log-concavity of cluster variables of type An and cluster monomials of type A2 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 A3, 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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