The Lonely Runner Conjecture turns 60

Guillem Perarnau; Oriol Serra

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The Lonely Runner Conjecture turns 60

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arxiv 2409.20160 v3 pith:LYV6XWZK submitted 2024-09-30 math.CO math.MGmath.NT

Guillem Perarnau , Oriol Serra This is my paper · ORCID

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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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