Representation of group elements as subsequence sums

Abstract:

Let G be a finite (additive written) abelian group of order n. Let w<inf>1</inf>, ..., w<inf>n</inf> be integers coprime to n such that w<inf>1</inf> + w<inf>2</inf> + ⋯ + w<inf>n</inf> ≡ 0 (mod n). Let I be a set of cardinality 2 n - 1 and let ξ = { x<inf>i</inf> : 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 { y<inf>1</inf>, ..., y<inf>n</inf> } of ξ such that y = w<inf>1</inf> y<inf>1</inf> + ⋯ + w<inf>n</inf> y<inf>n</inf>. Our result implies some known generalizations of the Erdo{combining double acute accent}s-Ginzburg-Ziv Theorem. © 2007 Elsevier B.V. All rights reserved.

Año de publicación:

2008

Keywords:

• Representation of groups
• Zero-sum sequences
• Erdo{combining double acute accent}s-Ginzburg-Ziv Theorem

Fuente:

scopus

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