On Davenport constant of finite abelian groups

2018/02/20 by Dongchun Han, Han, Dongchun
Engineering · Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1802.07196

openalex publication_date 2018/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

G be an additive finite abelian group. The Davenport constant \mathsf D(G) is the smallest integer t such that every sequence (multiset) S over G of length |S|≥ t has a non-empty zero-sum subsequence. Recently, B. Girard proved that for every fixed integer r > 1 the Davenport constant \mathsf D(C_n^r) is asymptotic to rn when n tends to infinity. In this paper, for every fixed positive integer r, we prove that \mathsf D(C_n^r)=rn+O((n)/(ln n)). This is an explicit version of the above result of B. Girard. Furthermore, we can get better estimates of the error term for some n of special types. Finally, we get an asymptotic result for some finite abelian groups of special types. Our proof combines a classical argument in the zero-sum theory together with some basic tools and results from analytic number theory.

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