Zero-sum problems and coverings by proper cosets

Authors:
Weidong Gao;Alfred Geroldinger
Affiliations:
Department of Computer Science and Technology, University of Petroleum, Shuiku Road, Changping, Beijing 102200, People's Republic of China;Institut für Mathematik, Karl-Franzens Universität, Heinrichstrasse 36, 8010 Graz, Austria
Venue:
European Journal of Combinatorics
Year:
2003

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Abstract

Let G be a finite Abelian group and D(G) its Davenport constant, which is defined as the maximal length of a minimal zero-sum sequence in G. We show that various problems on zero-sum sequences in G may be interpreted as certain covering problems. Using this approach we study the Davenport constant of groups of the form (Z/nZ)r, with n ≥ 2 and r ∈ N. For elementary p-groups G, we derive a result on the structure of minimal zero-sum sequences S having maximal length |S| = D(G).