Covering Radii of 3-Zonotopes and the Shifted Lonely Runner Conjecture
Abstract
We show that the shifted Lonely Runner Conjecture (sLRC) holds for 5 runners. We also determine that there are exactly 3 primitive tight instances of the conjecture, only two of which are tight for the non-shifted conjecture (LRC). Our proof is computational, relying on a rephrasing of the sLRC in terms of covering radii of certain zonotopes (Henze and Malikiosis), and on an upper bound for the (integer) velocities to be checked (Malikiosis et al.). As a tool for the proof, we devise an algorithm for bounding the covering radius of rational lattice polytopes, based on constructing dyadic fundamental domains.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Computational Geometry and Mesh Generation
Point processes and geometric inequalities
Publication details
- Journal / source
- Experimental Mathematics
- Publisher
- Informa UK Limited
- Pages
- 1–14
- Publication date
- 7 May 2026
- Language
- EN