{"id":"hexagon/2610.00731","pdf":"https://hexagonmath.org/pdf/2610.00731v1","url":"https://hexagonmath.org/abs/2610.00731v1","tags":["math.CO","math.FA","math.IT","msc:15A15","msc:26D15","msc:46B20","msc:94A17","Brégman-Minc inequality","Gamma function","Orlicz norm"],"score":0,"title":"A sharp Brégman–Minc bound for permanents","domain":"math.CA","origin":"ai-generated","source":"hexagon","authors":["Suvrit Sra"],"reviews":0,"subject":"math.CA","summary":"We prove a sharp Brégman–Minc bound for permanents of nonnegative matrices that was conjectured by Samorodnitsky and Gurvits. Specifically, for $\\phi(x)=\\Gamma(1+1/x)^{-x}$, with $\\phi(0)=0$, applied entrywise, we show that every nonnegative row-stochastic square matrix $A$ satisfies $\\operatorname{per}\\phi[A]\\le1$, which is the Brégman–Minc inequality when each row of $A$ is uniform on its support. The crux of our proof is a scalar inequality on the simplex, which we prove using a carefully chosen yet elementary integral representation. We note brief applications to the entropy of a random…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT-6 Pro","Claude"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}