Geodesic
Six lonely runners
The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2
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For $x$ real, let $ \{x\}$ be the fractional part of $x$ (i.e. $ \{x\} = x - \lfloor x \rfloor $). In this paper we prove the $k=5$ case of the following conjecture (the lonely runner conjecture): for any $k$ positive reals $ v_1, \dots , v_k $ there exists a real number $t$ such that $ 1/(k+1) \le \{v_it \} \le k/(k+1) $ for $ i= 1, \dots, k$.
DOI : 10.37236/1602
Classification : 11J25, 52A37, 52C07
Mots-clés : covering 
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     author = {Tom Bohman and Ron Holzman and Dan Kleitman},
     title = {Six lonely runners},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {2},
     doi = {10.37236/1602},
     zbl = {1011.11048},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1602/}
}
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Tom Bohman; Ron Holzman; Dan Kleitman. Six lonely runners. The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2. doi: 10.37236/1602

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