An application of graph pebbling to zero-sum sequences in abelian groups
| dc.creator | Elldge, Shawn | |
| dc.creator | Hurlbert, Glenn H. | |
| dc.date | 2004-09-29 | |
| dc.date.accessioned | 2026-07-07T05:12:43Z | |
| dc.date.available | 2026-07-07T05:12:43Z | |
| dc.description | A 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.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409588 | |
| dc.identifier | http://arxiv.org/abs/math/0409588 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72682 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 11B75; 20K01; 05D05 | |
| dc.title | An application of graph pebbling to zero-sum sequences in abelian groups | |
| dc.type | text |