{"id":"hexagon/2610.00599","pdf":"https://hexagonmath.org/pdf/2610.00599v1","url":"https://hexagonmath.org/abs/2610.00599v1","tags":["math.CO","msc:11B75","msc:20K01"],"score":0,"title":"A logarithmic error term for subset sums of zero-sum-free sets","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Chao Liu"],"reviews":0,"subject":"math.NT","summary":"For a positive integer $k$, let $f(k)$ be the minimum number of distinct nonempty subset sums of a zero-sum-free $k$-element set, where the minimum is taken over all finite abelian groups. We prove $f(k)\\ge \\frac{k^2}{2}-13k\\log(k+1)-116k$. Together with the classical upper bound, this gives $f(k)=k^2/2+O(k\\log k)$, with the optimal leading coefficient. As a consequence, the Olson constant of every finite abelian group $G$ satisfies $\\mathrm{Ol}(G)\\le\\sqrt{2|G|}+O(\\log|G|)$. The argument combines a triangular lower bound for repeated supports, a count using blocks of two and three copies,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}