Lemmens, Bas and Scheutzow, Michael and Sparrow, Colin (2007) Transitive actions of finite abelian groups of sup-norm isometries. European Journal of Combinatorics, 28 (4). pp. 1163-1179. ISSN 0195-6698. (doi:https://doi.org/10.1016/j.ejc.2006.02.003) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
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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.
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus|
|Depositing User:||Bas Lemmens|
|Date Deposited:||17 Nov 2011 16:10 UTC|
|Last Modified:||11 Jan 2012 12:22 UTC|
|Resource URI:||https://kar.kent.ac.uk/id/eprint/28442 (The current URI for this page, for reference purposes)|