A variant of Kemnitz conjecture

Authors:
W. D. Gao;R. Thangadurai
Affiliations:
Department of Computer Science and Technology, University of Petroleum, Shuiku Road, Changping, Beijing 102200, China;School of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
Venue:
Journal of Combinatorial Theory Series A
Year:
2004

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Abstract

For any integer n ≥ 3, by g(Zn ⊕ Zn) we denote the smallest positive integer t such that every subset of cardinality t of the group Zn ⊕ Zn contains a subset of cardinality n whose sum is zero. Kemnitz (Extremalprobleme für Gitterpunkte, Ph.D. Thesis, Technische Universität Braunschweig, 1982) proved that g(Zp ⊕ Zp) = 2p - 1 for p = 3, 5, 7. In this paper, as our main result, we prove that g(Zp ⊕ Zp) = 2p - 1 for all primes p ≥ 67.