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Transitive actions of finite abelian groups of sup-norm isometries
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Lemmens, Bas, Scheutzow, Michael and Sparrow, Colin. (2007) Transitive actions of finite abelian groups of sup-norm isometries. European Journal of Combinatorics, Vol.28 (No.4). pp. 1163-1179. ISSN 0195-6698
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Official URL: http://dx.doi.org/10.1016/j.ejc.2006.02.003
Abstract
There is a long-standing conjecture of Nussbaum which asserts that every finite set in R-n on which a cyclic group of sup-norm isometries acts transitively contains at most 2(n) points. The existing evidence supporting Nussbaum's conjecture only uses abelian properties of the group. It has therefore been suggested that Nussbaum's conjecture might hold more generally for abelian groups of sup-norm isometries. This paper provides evidence supporting this stronger conjecture. Among other results, we show that it, Gamma is an abelian group of sup-norm isometrics that acts transitively on a finite set X in R-n and Gamma contains no anticlockwise additive chains, then X has at most 2(n) points. (c) 2006 Elsevier Ltd. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | European Journal of Combinatorics |
| Publisher: | Academic Press |
| ISSN: | 0195-6698 |
| Date: | May 2007 |
| Volume: | Vol.28 |
| Number: | No.4 |
| Number of Pages: | 17 |
| Page Range: | pp. 1163-1179 |
| Identification Number: | 10.1016/j.ejc.2006.02.003 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/32137 |
Data sourced from Thomson Reuters' Web of Knowledge
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