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Lower Bounds on Lattice Covering Densities of Simplices

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 $343/264$.

preprint2022arXivOpen access
Miao FuFei XueChuanming Zong
math.COmath.MG
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Miao FuFei XueChuanming Zong

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