The Lonely Runner Conjecture turns 60
Combinatorics
2025-08-13 v3 Metric Geometry
Number Theory
Abstract
The Lonely Runner Conjecture originated in Diophantine approximation is turning 60. Even if the conjecture is still widely open, the flow of partial results, innovative tools and connections to different problems and applications has been steady on its long life. This survey attempts to give a panoramic view of the status of the problem, trying to highlight the contributions of the many papers that it has originated.
Cite
@article{arxiv.2409.20160,
title = {The Lonely Runner Conjecture turns 60},
author = {Guillem Perarnau and Oriol Serra},
journal= {arXiv preprint arXiv:2409.20160},
year = {2025}
}
Comments
42 pages; minor corrections and new Open Problems section