Chao Liu

A logarithmic error term for subset sums of zero-sum-free sets

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 $f(k)=k^2/2+O(k\log k)$, wi...