{"id":"hexagon/2610.00668","pdf":"https://hexagonmath.org/pdf/2610.00668v1","url":"https://hexagonmath.org/abs/2610.00668v1","tags":["msc:13F60","msc:05E16","Cluster Algebra"],"score":0,"title":"Counterexamples to log-concavity of cluster monomials and theta structure constants","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.CO","summary":"We disprove Conjectures 1.1 and 5.5 of Chen–Huang–Sun and the log-concavity assertions in Chen’s Conjecture 5.11 and Chen–Sun’s Conjecture 8.2 by constructing counterexamples for cluster monomials and theta structure constants in coefficient-free type \\(A_5\\).","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}