Log-concavity of cluster algebras of type $A_n$
Abstract
Abstract Okounkov (2003, Progr. Math. 213, 329–347) conjectured the log-concavity about the structure constants for many interesting basis from representation theory. For the cluster algebra, Gross et al. (2018, J. Amer. Math. Soc. 31, 497–608) 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 the theta basis of type $A_2$ are log-concave. As for larger generality, we conjecture the log-concavity of the structure constants for the theta basis of the cluster algebra.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Advanced Algebra and Geometry
Publication details
- Journal / source
- Nagoya Mathematical Journal
- Publisher
- Cambridge University Press (CUP)
- Volume
- 261
- Publication date
- 1 January 2026
- Language
- EN