2014/07/12 by Guillem Perarnau, Perarnau, Guillem, Oriol Serra +1 · 1 citation
Computer Science · Mathematics · #Artificial Intelligence in Games #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1407.3381
openalex publication_date 2014/07/12 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
The Lonely Runner Conjecture was posed independently by Wills and Cusick and\nhas many applications in different mathematical fields, such as diophantine\napproximation. This well-known conjecture states that for any set of runners\nrunning along the unit circle with constant different speeds and starting at\nthe same point, there is a moment where all of them are far enough from the\norigin. We study the correlation among the time that runners spend close to the\norigin. By means of these correlations, we improve a result of Chen on the gap\nof loneliness and we extend an invisible runner result of Czerwinski and\nGrytczuk. In the last part, we introduce dynamic interval graphs to deal with a\nweak version of the conjecture thus providing some new results.\n