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arxiv: 2409.20160 · v3 · pith:LYV6XWZKnew · submitted 2024-09-30 · 🧮 math.CO · math.MG· math.NT

The Lonely Runner Conjecture turns 60

Guillem Perarnau , Oriol Serra This is my paper
classification 🧮 math.CO math.MGmath.NT
keywords conjecturelonelyoriginatedrunnerapplicationsapproximationattemptsbeen
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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.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Covering radii of $3$-zonotopes and the shifted Lonely Runner Conjecture

    math.CO 2025-06 accept novelty 7.0

    The shifted Lonely Runner Conjecture holds for five runners, with exactly three primitive tight instances, two of which are also tight for the original conjecture.