Weighted sequences in finite cyclic groups


Let p > 7 be a prime, let G = Z/pZ, and let S1 = ∏i=1p gi and S2 = ∏i=1p hi be two sequences with terms from G. Suppose that the maximum multiplicity of a term from either S1 or S2 is at most (2p + 1)/5. Then we show that, for each g ∈ G, there exists a permutation σ of 1, 2,...,p such that g = Σi=1p (gi · h σ(i)). The question is related to a conjecture of A. Bialostocki concerning weighted subsequence sums and the Erdos-Ginzburg-Ziv Theorem.

Publication Title

Applied Mathematics E - Notes

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