论文标题
晶格的下限覆盖了简单的密度
Lower Bounds on Lattice Covering Densities of Simplices
论文作者
论文摘要
本文通过研究Abelian Cayley Digraphs的度直径问题，为晶格提供了新的下限，覆盖了简单的密度。特别是，它证明了四面体的任何格子覆盖物的密度至少为$ 25/18 $，并且任何四维单纯形的晶格覆盖率的密度至少为$ 343/264 $。
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 $25/18$ and the density of any lattice covering of a four-dimensional simplex is at least $343/264$.
