Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Inquiries about lonely runner conjecture

  1. Nov 13, 2016 #1
    Here is the Wikipedia article on the lonely runner conjecture

    https://en.m.wikipedia.org/wiki/Lonely_runner_conjecture#

    I have some inquires about it.

    Firstly I am right in thinking that "pair wise distinct" means that the speed of all runners are different?

    Also does every runner have to be at least 1/k (k is the number of runners) from all the other runners simultaneously? Or can runners achieve "loneliness" at a certain time even whilst other runners have not?

    Furthermore, once a runner achieves "loneliness" is it maintained? In other words say a runner is lonely, does it stay lonely even if the distance between it and the other runners decreases to become smaller than 1/k afterwards?
     
    Last edited: Nov 13, 2016
  2. jcsd
  3. Nov 13, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Yes. If two runners have the same speed, then they are never lonely, and the problem gets trivial.

    Runners can achieve loneliness independent of other runners (otherwise the problem would be trivial again).
    Sure.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Inquiries about lonely runner conjecture
  1. The Motionless Runner (Replies: 2)

  2. A conjecture (Replies: 9)

Loading...