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Algebra |
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Authors: Deepak Ponvel Chermakani
Consider the problem of finding the time T at which none of the n-1 moving runners are in the arc Z of length 2/n centered at the stationary runner 0 in an instance of the Shifted Lonely Runner Conjecture (SLRC). We show two important results for prime n and for large n. Firstly, there exist atleast 3 time intervals during which atmost 1 moving runner is in Z for the SLRC, and, there exist atleast 4(n-1) time intervals during which atmost 1 moving runner is in Z for the LRC. Secondly, for both the SLRC and the LRC considered separately, there are atleast 2 different moving runners which prevent the loneliness of runner 0 by being the atmost one runner in Z at some time.
Comments: 3 Pages. 3 theorems.
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[v1] 2026-09-28 20:54:26
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