单纯形晶格覆盖密度的下界

SIAM J. Discret. Math. Pub Date : 2022-02-12 DOI:10.1137/22m1514155

Miao Fu, F. Xue, C. Zong

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引用次数: 2

摘要

本文通过对阿贝尔Cayley有向图的度-直径问题的研究，给出了简单点格覆盖密度的新的下界。特别地，证明了四面体的任何晶格覆盖的密度至少为$25/18$，四维单纯形的任何晶格覆盖的密度至少为$343/264$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 $343/264$.

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SIAM J. Discret. Math.

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