On Hadwiger's covering functional for the simplex and the cross-polytope

Autor:	Xue, Fei, Lian, Yanlu, Zhang, Yuqin
Rok vydání:	2021
Předmět:	Mathematics - Metric Geometry 52C17 G.2.1
Druh dokumentu:	Working Paper
Popis:	In 1957, Hadwiger made a conjecture that every $n$-dimensional convex body can be covered by $2^n$ translations of its interior. The Hadwiger's covering functional $\gamma_m(K)$ is the smallest positive number $r$ such that $K$ can be covered by $m$ translations of $rK$. Due to Zong's program, we study the Hadwiger's covering functional for the simplex and the cross-polytope. In this paper, we give upper bounds for the Hadwiger's covering functional of the simplex and the cross-polytope. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2108.13277 Zobrazit plný text záznamu View this record from Arxiv