On the covering radius of lattice zonotopes and its relation to view-obstructions and the lonely runner conjecture

Abstract

The goal of this paper is twofold; first, show the equivalence between certain problems in geometry, such as view-obstruction and billiard ball motions, with the estimation of covering radii of lattice zonotopes. Second, we will estimate upper bounds of said radii by virtue of the Flatness Theorem. These problems are similar in nature with the famous lonely runner conjecture.

18 pages, 1 figure

References in corpus (1)

• Rotations by roots of unity and Diophantine approximation

Cited by in corpus (4)

• The covering radius and a discrete surface area for non-hollow simplices
• Linearly-exponential checking is enough for the Lonely Runner Conjecture and some of its variants
• Computing the covering radius of a polytope with an application to lonely runners
• The structure of Lonely Runner spectra