View-obstruction: a shorter proof for 6 lonely runners
type: Item
instance of: scholarly article
title: View-obstruction: a shorter proof for 6 lonely runners
zbMATH Open document ID: 1061.11036
author: Jérôme Renault
published in: Discrete Mathematics
publication date: 2004-11-18T00:00:00Z
full work available at URL: https://basepub.dauphine.fr/handle/123456789/6201
review text: The lonely runner conjecture (see, for example, \textit{W. Bienia}, \textit{L. Goddyn}, \textit{P. Gvozdjak}, \textit{A. Sebö} and \textit{M. Tarsi} [J. Comb. Theory, Ser. B 72, No. 1, 1--9 (1998; Zbl 0910.05064)]) can be stated as follows: Let \(v_1,\dots, v_s\) be positive integers. There is a real number \(t\) such that \(\{tv_i\}\in [1/(s+ 1),s/(s+ 1)]\) for all \(i\in \{1,\dots, s\}\). It is well-known that it is true for \(s= 2,3,4,5\). In the present paper, the author gives a new proof of this conjecture for the case \(s= 5\), basing on a careful study of the different congruence classes modulo 6 of the numbers \(v_1,\dots, v_5\). Moreover, the author also gives very simple and elementary proofs for the cases \(s= 2,3,4\).
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 11A99
zbMATH DE Number: 2116258
zbMATH Keywords: Lonely runner conjecture
zbMATH Keywords: View-obstruction
Wikidata QID: Q56766746
reviewed by: Yaochen Zhu
MaRDI profile type: Publication
OpenAlex ID: W2125641832
cites work: Untere Schranken für zwei diophantische Approximations-Funktionen
cites work: Flows, view obstructions, and the lonely runner
cites work: Six lonely runners
cites work: View-obstruction problems
cites work: View-obstruction problems in \(n\)-dimensional geometry
cites work: View-Obstruction Problems. II
cites work: View-obstruction problems. III
cites work: Zwei Sätze über inhomogene diophantische Approximation von Irrationalzahlen
DBLP publication ID: journals/dm/Renault04
DOI: 10.1016/J.DISC.2004.06.008
description: scientific article; zbMATH DE number 2116258