Improved lower bound on generalized Erdos-Ginzburg-Ziv constants

2017/12/06 by Jesse Geneson, Geneson, Jesse
Mathematics · #Graph theory and applications #Limits and Structures in Graph Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1712.02069

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) > (n)/(2)[(5)/(4)-O(n^-(3)/(2))]^r and s_{k n}(C_n^r) > (k n)/(4) [1+(1)/(e k)-O((1)/(n))]^r for k > 2. In this note, we sharpen their general bound by showing that s_{k n}(C_n^r) > (k n)/(4) [1+\frac(k-1)^(k-1)k^k-O((1)/(n))]^r for k > 2.

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