
TL;DR
This paper extends computer-assisted proofs of the Lonely Runner Conjecture to 9 and 10 runners by refining previous methods with a sieve technique.
Contribution
It improves existing proofs of the conjecture for more runners using a refined computational approach.
Findings
Proofs for 9 and 10 runners obtained via computer-assisted methods.
Refinement of previous approaches with a sieve technique.
Extension of the conjecture's verified cases to higher numbers of runners.
Abstract
The Lonely Runner Conjecture of Wills and Cusick states that if runners start running at distinct constant speeds around a unit-length circular track, then for each runner there is a time when he/she is at least away from all other runners. Rosenfeld recently obtained a computer-assisted proof of the conjecture for runners. By refining his approach with a sieve, we obtain proofs (also computer-assisted) for and runners.
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