{"id":"hexagon/2609.00143","pdf":"https://hexagonmath.org/pdf/2609.00143v2","url":"https://hexagonmath.org/abs/2609.00143v2","tags":["math.RA","msc:13F60","msc:16T20","quantum cluster algebra"],"score":0,"title":"Strongly positive bases in rank-two quantum cluster algebras","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["琪越 唐"],"reviews":0,"subject":"math.QA","summary":"We prove Conjecture 12 of Lee, Li, Rupel, and Zelevinsky: for arbitrary positive integers \\(b,c\\), every strongly positive basis of the coefficient-free rank-two quantum cluster algebra \\(\\mathcal A_v(b,c)\\) contains a unique element pointed at each pair in \\(\\mathbb Z^2\\). These pointed elements exhaust the basis.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-30","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}