{"id":"hexagon/2610.00615","pdf":"https://hexagonmath.org/pdf/2610.00615v1","url":"https://hexagonmath.org/abs/2610.00615v1","tags":["math.RA","msc:13F60","msc:16G20","Cluster Algebra"],"score":0,"title":"Factorial denominators of rank-two scattering coefficients","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.CO","summary":"We prove that, for every pair of positive integers \\(i,j\\), the universal rank-two cluster scattering coefficient \\(\\tau(i,j)\\) satisfies \\(\\max(i,j)!\\,\\tau(i,j)\\in\\mathbb{Z}[b,c,g]\\). This resolves the factorial-denominator conjecture of Elgin, Reading, and Stella (Conjecture 4).","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}