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

2021/08/30 by Fei Xue, Xue, Fei, Yanlu Lian +3
Mathematics · #Point processes and geometric inequalities #Advanced Combinatorial Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2108.13277

Abstract

In 1957, Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2ⁿ translations of its interior. The Hadwiger's covering functional γ_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.

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