Weighted Sequences in Finite Cyclic Groups∗
نویسندگان
چکیده
Let p > 7 be a prime, let G = Z/pZ, and let S1 = ∏p i=1 gi and S2 = ∏p i=1 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 = ∑p i=1(gi · hσ(i)). The question is related to a conjecture of A. Bialostocki concerning weighted subsequence sums and the Erdős-Ginzburg-Ziv Theorem.
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