Year: 2026
Type: preprint
Abstract: We prove that every cluster monomial of type A_n is log-concave and unimodal with respect to its Laurent expansion in a fan initial cluster. We derive a coefficient formula for laminar interval products arising from compatible diagonals in the polygon model. This gives partial affirmative answers to the log-concavity conjecture of Chen-Huang-Sun and the unimodality conjecture of Chen. Our result for cluster A-varieties also complements Shen's study on the supports of products of canonical basis elements for cluster X-varieties of type A_n.
Source: arXiv (Cornell University)
Author: Chen, Zhichao
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221046145