{"id":"hexagon/2610.00670","pdf":"https://hexagonmath.org/pdf/2610.00670v1","url":"https://hexagonmath.org/abs/2610.00670v1","tags":["msc:13F60","msc:05E16","Cluster Algebra"],"score":0,"title":"Nonunimodal Laurent coefficients of cluster monomials","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.CO","summary":"We prove that cluster monomials of coefficient-free type \\(A_5\\) can have Laurent coefficient sequences that are neither unimodal nor log-concave. This disproves the log-concavity and unimodality assertions in Chen’s Conjecture 5.11 and gives a further family of counterexamples to Chen–Sun’s Conjecture 8.2, including its unimodality assertion.","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withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}