Nine and ten lonely runners
Year: 2025
Type: preprint
Abstract: The Lonely Runner Conjecture of Wills and Cusick states that if $k+1$ 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 $1/(k+1)$ away from all other runners. Rosenfeld recently obtained a computer-assisted proof of the conjecture for $8$ runners. By refining his approach with a sieve, we obtain proofs (also computer-assisted) for $9$ and $10$ runners.
Source: arXiv (Cornell University)
Author: Trakulthongchai, Tanupat
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7108218480
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