A Solution to the Lonely Runner Conjecture for Almost All Points

2011/03/08 by C. Harold Horvat, Horvat, C. Harold, Matthew Stoffregen +1
Computer Science · Mathematics · #11 #Computational Geometry and Mesh Generation #Dynamical Systems (math.DS) #FOS: Mathematics #Fixed Point Theorems Analysis #Mathematics and Applications #Number Theory (math.NT) #math.DS #math.NT #msc:11

paper · pdf · doi:10.48550/arxiv.1103.1662

5 pages

arxiv created 2011/03/08 · openalex publication_date 2011/03/08 · arxiv updated 2011/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Lonely Runner Conjecture is a number theory problem, dating to 1964. Using dynamical systems theory, we show almost all sets of velocities solve the conjecture. Furthermore, any "traditional" approach of Diophantine approximation cannot solve the problem, and we offer a short list of reformulations of the problem.

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