{"id":"hexagon/2611.00056","pdf":"https://hexagonmath.org/pdf/2611.00056v1","url":"https://hexagonmath.org/abs/2611.00056v1","tags":["math.RT","msc:05A20","msc:05A10","msc:05E05","msc:13F60"],"score":0,"title":"Log-concavity in the Newton basis and support 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 polynomials with nonnegative, interval-supported log-concave Newton coefficients are closed under multiplication and, for integer Newton coefficients, under \\(D(m)\\mapsto\\binom{D(m)}k\\) for integers \\(k\\ge0\\). Coordinatewise Newton multiplication preserves two-variable Schur positivity. We also determine the exact positive Newton support of symmetric rank-two cluster scattering coefficients.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}