SU\G(𝔾)/K·U

LONELY RUNNERS IN FUNCTION FIELDS

Sam Chow, Luka Rimanić

Type: Article

Publication Date: 2019-01-01

Citations: 1

DOI: https://doi.org/10.1112/s002557931900007x

Abstract

The lonely runner conjecture, now over fifty years old, concerns the following problem. On a unit length circular track, consider $m$ runners starting at the same time and place, each runner having a different constant speed. The conjecture asserts that each runner is lonely at some point in time, meaning distance at least $1/m$ from the others. We formulate a function field analogue, and give a positive answer in some cases in the new setting.

Locations

  • arXiv (Cornell University) - View - PDF
  • Warwick Research Archive Portal (University of Warwick) - View - PDF
  • Oxford University Research Archive (ORA) (University of Oxford) - View - PDF
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  • Mathematika - View

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Works Cited by This (31)

Action Title Year Authors
+ Number Fields and Function Fields—Two Parallel Worlds 2005 Gerard van der Geer
B.J. Moonen
René Schoof
+ Extremal Combinatorics: With Applications in Computer Science 2001 Stasys Jukna
+ Random Matrices, Frobenius Eigenvalues, and Monodromy 1998 Nicholas M. Katz
Peter Sarnak
+ Theorie der algebraischen Functionen einer VerÀnderlichen. 1882 H. Wéber
Richard Dedekind
+ PDF Chat On the Bateman–Horn conjecture for polynomials over large finite fields 2016 Alexei Entin
+ The chromatic number of random Cayley graphs 2013 Noga Alon
+ Flows, View Obstructions, and the Lonely Runner 1998 Wojciech Bienia
Luis Goddyn
Pavol Gvozdjak
Andrås Sebö
Michael Tarsi
+ View-obstruction problems. II 1982 Thomas W. Cusick
+ Random runners are very lonely 2012 Sebastian CzerwiƄski
+ Invisible runners in finite fields 2008 Sebastian CzerwiƄski
JarosƂaw Grytczuk