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Correlation among runners and some results on the lonely runner conjecture

Author
Perarnau, G.; Serra, O.
Type of activity
Journal article
Journal
Electronic journal of combinatorics
Date of publication
2016-10-03
Volume
23
Number
1
First page
1
Last page
22
Repository
http://hdl.handle.net/2117/101787 Open in new window
URL
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p50/pdf Open in new window
Abstract
The Lonely Runner Conjecture, posed independently by Wills and by Cusick, states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a time where all of them are far enough from the origin. We study the correlation among the time that runners spend close to the origin. By means of these correlations, we improve a result of Chen on the gap of loneliness. In the last part, we introduce dynamic interval graphs to deal wit...
Citation
Perarnau, G., Serra, O. Correlation among runners and some results on the lonely runner conjecture. "Electronic journal of combinatorics", 3 Octubre 2016, vol. 23, núm. 1, p. 1-22.
Keywords
Lonely Runner Conjecture
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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