(Q6671695)

English

lonely runner conjecture

number-theoretic conjecture that states that 𝑘 people running around a circular track with distinct speeds will each be, at some point, separated by ¹⁄ₖ from every other runner

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Lonely runner.gif
256 × 256; 1.15 MB

example of a case of the conjecture with 6 runners: black runners have not yet been lonely; white arcs, of length ²⁄₆, indicate that a runner is currently lonely; yellow runners have experienced loneliness (English)

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defining formula

\forall 0<v_{1}<v_{2}<\dotsb <v_{n-1}\exists t>0\forall i\in \{1,\dotsc ,n-1\}\colon {\frac {1}{n}}\leq \operatorname {frac} (v_{i}t)\leq 1-{\frac {1}{n}}

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in defining formula

\operatorname {frac}

symbol represents

fractional part

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maintained by WikiProject

WikiProject Mathematics

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Microsoft Academic ID

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1 reference

26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

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