A Note on Lacunary Lonely Runners
This paper has been withdrawn by the author.
See the erratum below.
Stefan Steinerberger
Department of Financial Mathematics
University of Linz
Altenbergstraße 69
4040 Linz
Austria
Abstract:
We give a simple argument proving the lonely runner conjecture in the
case where the speed of the runners forms a certain lacunary sequence.
This improves an earlier result by Pandey, and is then used to derive
that for each number of runners the lonely runner conjecture is true
for a set of nonzero measure in a natural probability space.
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erratum
Received September 9 2010;
revised version received September 19 2010.
Published in Journal of Integer Sequences, December 6 2010.
Withdrawn, January 3 2011.
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