Correlation among runners and some results on the lonely runner conjecture
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/101787
Tipus de documentArticle
Data publicació2016-10-03
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
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 with a weak version of the conjecture thus providing a new result related to the invisible runner theorem of Czerwi´nski and Grytczuk.
CitacióPerarnau, 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.
ISSN1077-8926
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
16_02_15_lonely_EJC.pdf | 415,4Kb | Visualitza/Obre |