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Two Zero-Sum Problems and Multiple Properties

✍ Scribed by W.D Gao

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
163 KB
Volume
81
Category
Article
ISSN
0022-314X

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✦ Synopsis

In this paper we consider the following open problems: Conjecture 0.1. Let S be a sequence of 3n&3 elements in C n Γ„ C n . If S contains no nonempty zero-sum subsequence of length not exceeding n, then S consists of three distinct elements, each appearing n&1 times.

Conjecture 0.2. Let S be a sequence of 4n&4 elements in C n Γ„ C n . If S contains no zero-sum subsequence of length n, then S consists of four distinct elements, each appearing n&1 times.

We show that both Conjecture 0.1 and Conjecture 0.2 are multiplicative, i.e., if Conjecture 0.1 (Conjecture 0.2) holds both for n=k and n=l then it holds also for n=kl.

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