Covering functionals of convex polytopes with few vertices

TL;DR

This paper establishes new upper bounds for covering functionals of convex polytopes in high-dimensional spaces, relying solely on the number of vertices, thereby advancing understanding of geometric covering properties.

Contribution

It introduces refined techniques to derive bounds for covering functionals of convex polytopes using only vertex count, improving previous estimates.

Findings

New upper bounds for covering functionals based on vertex count

Techniques refined from recent related work

Bounds applicable in high-dimensional spaces

Abstract

By using elementary yet interesting observations and refining techniques used in a recent work by Fei Xue et al., we present new upper bounds for covering functionals of convex polytopes in $\mathbb{R}^n$ with few vertices. In these estimations, no information other than the number of vertices of the convex polytope is used.