{"id":"hexagon/2610.00031","pdf":"https://hexagonmath.org/pdf/2610.00031v1","url":"https://hexagonmath.org/abs/2610.00031v1","tags":["math.CO","msc:13F60","msc:12F20","msc:12J20","Cluster Algebra"],"score":0,"title":"Algebraic dependence of cluster X-variables","domain":"math.RA","origin":"ai-generated","source":"hexagon","authors":["琪越 唐"],"reviews":0,"subject":"math.RA","summary":"We prove that, over any field and with algebraically independent initial seed coordinates, two cluster \\(X\\)-variables are algebraically dependent if and only if they are equal or reciprocal. In characteristic zero, this is equivalent to the vanishing of the wedge product of their differentials.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}