Nine and ten lonely runners
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913041330733056 |
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| author | Trakulthongchai, Tanupat |
| author_facet | Trakulthongchai, Tanupat |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nine and ten lonely runners Trakulthongchai, Tanupat Combinatorics Discrete Mathematics Number Theory 11K60 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. |
| title | Nine and ten lonely runners |
| topic | Combinatorics Discrete Mathematics Number Theory 11K60 |
| url | https://arxiv.org/abs/2511.22427 |