Improved lower bound on generalized Erdos-Ginzburg-Ziv constants

Abstract

If $G$ is a finite Abelian group, define $s_k(G)$ to be the minimal $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. Recently Bitz et al. proved that if $n=exp(G)$, then $s_{2n}(C_n^r)>\frac{n}{2}[\frac{5}{4}-O(n^{-\frac{3}{2}}){]}^r$ and $s_{kn}(C_n^r)>\frac{kn}{4}[1+\frac{1}{ek}-O(\frac{1}{n}){]}^r$ for $k>2$. In this note, we sharpen their general bound by showing that $s_{kn}(C_n^r)>\frac{kn}{4}[1+\frac{(k-1{)}^{(k-1)}}{k^k}-O(\frac{1}{n}){]}^r$ for $k>2$.

3 pages