Invisible runners in finite fields

@article{Czerwinski2008InvisibleRI,
  title={Invisible runners in finite fields},
  author={Sebastian Czerwinski and Jaroslaw Grytczuk},
  journal={Inf. Process. Lett.},
  year={2008},
  volume={108},
  pages={64-67}
}
  • Sebastian Czerwinski, Jaroslaw Grytczuk
  • Published in Inf. Process. Lett. 2008
  • Mathematics, Computer Science
  • Suppose k runners having different constant speeds run laps on a circular track of unit length. The Lonely Runner Conjecture states that, sooner or later, any given runner is at distance at least 1/k from all the other runners. We prove here that the statement of the conjecture holds if we eliminate only one chosen runner. The proof uses a simple double-counting argument in the setting of finite fields. We also demonstrate that the original problem reduces to an analogous statement in… CONTINUE READING

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