Journal Article

ZERO-SUM PROBLEMS IN FINITE ABELIAN GROUPS AND AFFINE CAPS

Yves Edel, Christian Elsholtz, Alfred Geroldinger, Silke Kubertin and Laurence Rackham

in The Quarterly Journal of Mathematics

Volume 58, issue 2, pages 159-186
Published in print June 2007 | ISSN: 0033-5606
Published online May 2007 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/ham003
ZERO-SUM PROBLEMS IN FINITE ABELIAN GROUPS AND AFFINE CAPS

Show Summary Details

Preview

Abstract

For a finite abelian group G, let [math] (G) denote the smallest integer l such that every sequence S over G of length | S| ≥ l has a zero-sum subsequence of length exp (G). We derive new upper and lower bounds for [math] (G), and all our bounds are sharp for special types of groups. The results are not restricted to groups G of the form [math], but they respect the structure of the group. In particular, we show [math] for all odd n, which is sharp if n is a power of 3. Moreover, we investigate the relationship between extremal sequences and maximal caps in finite geometry.

Journal Article.  0 words. 

Subjects: Pure Mathematics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content. subscribe or login to access all content.