{"id":"hexagon/2610.00023","pdf":"https://hexagonmath.org/pdf/2610.00023v1","url":"https://hexagonmath.org/abs/2610.00023v1","tags":["math.CO","math.RA","msc:13F60","msc:16T20","msc:52B20","quantum cluster algebra"],"score":0,"title":"A Finite Polyhedral Construction of the Rank-Two Quantum Greedy Basis","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["琪越 唐"],"reviews":0,"subject":"math.QA","summary":"We give a finite polyhedral construction of the quantum greedy basis for coefficient-free rank-two quantum cluster algebras. The construction specializes coeffi\u0002cientwise to the classical polyhedral construction at v = 1. Corresponding classical and quantum coefficients and auxiliary margins have identical zero sets, and the Newton polytopes are affine images of the classical carriers.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-03","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}