Lower Bounds on Lattice Covering Densities of Simplices
Metric Geometry
2022-02-15 v1 Combinatorics
Abstract
This paper presents new lower bounds for the lattice covering densities of simplices by studying the Degree-Diameter Problem for abelian Cayley digraphs. In particular, it proves that the density of any lattice covering of a tetrahedron is at least and the density of any lattice covering of a four-dimensional simplex is at least .
Keywords
Cite
@article{arxiv.2202.06025,
title = {Lower Bounds on Lattice Covering Densities of Simplices},
author = {Miao Fu and Fei Xue and Chuanming Zong},
journal= {arXiv preprint arXiv:2202.06025},
year = {2022}
}
Comments
16 pages, 4 figures