1. Log-concavity of cluster algebras of type $A_n$
- Author
-
Chen, Zhichao, Huang, Guanhua, and Sun, Zhe
- Subjects
Mathematics - Representation Theory ,Mathematics - Combinatorics ,Mathematics - Geometric Topology ,13F60, 05E99, 16S34 - Abstract
After Gross, Hacking, Keel, Kontsevich [GHKK18] introduced the theta basis which is shown to be indexed by its highest term exponent in cluster variables of any given seed, we are interested in all the non-vanishing exponents in these cluster variables. We prove that the coefficients of the exponents of any cluster variable of type $A_n$ are log-concave. We show that the cluster monomials of $A_2$ type are log-concave. As for larger generality, we conjecture that the log-concavity of cluster monomials is also true., Comment: 26 pages, 10 figures
- Published
- 2024