An application of graph pebbling to zero-sum sequences in abelian groups

dc.creatorElldge, Shawn
dc.creatorHurlbert, Glenn H.
dc.date2004-09-29
dc.date.accessioned2026-07-07T05:12:43Z
dc.date.available2026-07-07T05:12:43Z
dc.descriptionA sequence of elements of a finite group G is called a zero-sum sequence if it sums to the identity of G. The study of zero-sum sequences has a long history with many important applications in number theory and group theory. In 1989 Kleitman and Lemke, and independently Chung, proved a strengthening of a number theoretic conjecture of Erdos and Lemke. Kleitman and Lemke then made more general conjectures for finite groups, strengthening the requirements of zero-sum sequences. In this paper we prove their conjecture in the case of abelian groups. Namely, we use graph pebbling to prove that for every sequence (g_k)_{k=1}^{|G|} of |G| elements of a finite abelian group G there is a nonempty subsequence (g_k)_{k in K} such that sum_{k in K}g_k=0_G and sum_{k in K}1/|g_k|\le 1, where |g| is the order of the element g in G.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0409588
dc.identifierhttp://arxiv.org/abs/math/0409588
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72682
dc.subjectCombinatorics
dc.subjectGroup Theory
dc.subject11B75; 20K01; 05D05
dc.titleAn application of graph pebbling to zero-sum sequences in abelian groups
dc.typetext

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