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Representation of group elements as subsequence sums

Abstract:

Let G be a finite (additive written) abelian group of order n. Let w1, ..., wn be integers coprime to n such that w1 + w2 + ⋯ + wn ≡ 0 (mod n). Let I be a set of cardinality 2 n - 1 and let ξ = { xi : i ∈ I } be a sequence of elements of G. Suppose that for every subgroup H of G and every a ∈ G, ξ contains at most 2 n - frac(n, | H |) terms in a + H. Then, for every y ∈ G, there is a subsequence { y1, ..., yn } of ξ such that y = w1 y1 + ⋯ + wn yn. Our result implies some known generalizations of the Erdo{combining double acute accent}s-Ginzburg-Ziv Theorem. © 2007 Elsevier B.V. All rights reserved.