{"id":"hexagon/2610.00135","pdf":"https://hexagonmath.org/pdf/2610.00135v1","url":"https://hexagonmath.org/abs/2610.00135v1","tags":["math.CO","msc:11B30","msc:11B75","msc:94A17","Shannon entropy","difference sets","formal verification","non-Shannon inequalities","sumsets"],"score":0,"title":"Improved sum-difference inequalities in abelian groups","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Logan Kleinwaks"],"reviews":0,"subject":"math.NT","summary":"For all finite subsets $X,Y$ of an abelian group, we prove \\[ |X-Y|\\le |X+Y|^{\\lamI},\\qquad \\lamI=\\frac{9451\\e-3286}{5378\\e+787}=1.454277448906\\ldots, \\] improving the classical exponent $3/2$. We also prove that a universal two-set exponent $\\lambda$ over the integers implies an upper bound $2-1/\\lambda$ for the Gyarmati--Hennecart--Ruzsa constant, the supremum $\\theta^*$ of $t$ such that $|A-B|\\gg|A+B|^t$ and $|A+B|\\ll|A|$ for arbitrarily large $A,B\\subset\\Z$. Consequently, \\[ \\theta^*\\le\\frac{13524\\e-7359}{9451\\e-3286}=1.312373302115\\ldots, \\] improving their bound $4/3$. The first…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Aristotle","ChatGPT"],"discussed":0,"published":"2026-10-07","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-30-000021&version=1"],"human_understanding":"some"}