Six Lonely Runners

2001/02/06 by Tom Bohman, Ron Holzman, Dan Kleitman · 40 citations
Mathematics · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Conjecture #Mathematics #Combinatorics #Real number #Discrete mathematics

paper · pdf · doi:10.37236/1602

published in The Electronic Journal of Combinatorics 8(2) (Electronic Journal of Combinatorics)

openalex publication_date 2001/02/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For x real, let \x\ be the fractional part of x (i.e. \x\ = x - \lfloor x \rfloor ). In this paper we prove the k=5 case of the following conjecture (the lonely runner conjecture): for any k positive reals v₁, … , v_k there exists a real number t such that 1/(k+1) ≤ \v_it \ ≤ k/(k+1) for i= 1, …, k.

Citations

• Flows, View Obstructions, and the Lonely Runner
• View-obstruction problems, III
• View-obstruction problems
• Untere Schranken f�r zwei diophantische Approximations-Funktionen
• View-obstruction problems in n-dimensional geometry

Cited by

• The Lonely Runner with Seven Runners
• The lonely runner problem for many runners
• Correlation Among Runners and Some Results on the Lonely Runner Conjecture
• Lonely runner conjecture [wikipedia]