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Linearly exponential checking is enough for the lonely runner conjecture and some of its variants

Abstract: Tao (2018) showed that in order to prove the Lonely Runner Conjecture (LRC) up to n + 1 runners it suffices to consider positive integer velocities in the order of nO(n2). Using the zonotopal reinterpretation of the conjecture due to the first and third authors (2017) we here drastically improve this result, showing that velocities up to n2+1n-1

 Fuente: Forum of Mathematics, Sigma, 2025, 13(e164), 1-32

 Publisher: Cambridge University Press

 Publication date: 01/10/2025

 No. of pages: 32

 Publication type: Article

 DOI: 10.1017/fms.2025.10107

 ISSN: 2050-5094

 Spanish project: PID2022-137283NB-C21

Authorship

MALIKIOSIS, ROMANOS DIOGENES

SCHYMURA, MATTHIAS