Deep Lattice Points in Zonotopes, Lonely Runners, and Lonely Rabbits
Deep Lattice Points in Zonotopes, Lonely Runners, and Lonely Rabbits
Abstract Let $P \subseteq {\mathbb {R}}^{d}$ be a polytope and let $\textbf {w}$ be an interior point of $P$. The coefficient of asymmetry$\operatorname {ca}(P,\textbf {w}):= \min \{ \lambda \geq 1: \textbf {w} - P \subseteq \lambda (P - \textbf {w}) \}$ of $P$ about $\textbf {w}$ has been studied extensively …