The lonely runner with seven runners

dc.creatorBarajas, J.
dc.creatorSerra, O.
dc.date2007-10-24
dc.date.accessioned2026-07-07T08:38:25Z
dc.date.available2026-07-07T08:38:25Z
dc.descriptionSuppose $k+1$ runners having nonzero constant speeds run laps on a unit-length circular track starting at the same time and place. A runner is said to be lonely if she is at distance at least $1/(k+1)$ along the track to every other runner. The lonely runner conjecture states that every runner gets lonely. The conjecture has been proved up to six runners ($k\le 5$). A formulation of the problem is related to the regular chromatic number of distance graphs. We use a new tool developed in this context to solve the first open case of the conjecture with seven runners.
dc.identifierhttps://arxiv.org/abs/0710.4495
dc.identifierhttp://arxiv.org/abs/0710.4495
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140726
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject11B75, 11J71
dc.titleThe lonely runner with seven runners
dc.typetext

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