Nine and ten lonely runners
arXiv:2511.224278.85 citationsh-index: 1
Predicted impact top 37% in CO · last 90 daysOriginality Synthesis-oriented
AI Analysis
Advances a long-standing combinatorial conjecture for two additional cases, but the approach is incremental and computer-dependent.
The authors prove the Lonely Runner Conjecture for 9 and 10 runners using a computer-assisted sieve method, extending previous results for 8 runners.
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.