English

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

Representation Theory 2026-05-14 v4 Combinatorics Rings and Algebras

Abstract

The log-concavity of cluster variables of type AnA_n and cluster monomials of type A2A_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 A3A_3, a substantially more intricate case. Moreover, we refine and extend this conjecture by considering the unimodality and the strongly isomorphism of cluster algebras.

Keywords

Cite

@article{arxiv.2601.21496,
  title  = {Log-concavity and unimodality of cluster monomials of type $A_3$},
  author = {Zhichao Chen},
  journal= {arXiv preprint arXiv:2601.21496},
  year   = {2026}
}

Comments

24 pages, 4 figures. Minor typos have been corrected