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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 25/1825/18 and the density of any lattice covering of a four-dimensional simplex is at least 343/264343/264.

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