On Lattice Coverings by Simplices
Fei Xue, Chuanming Zong
TL;DR
This paper establishes a new lower bound on the lattice covering density by n-dimensional simplices, advancing understanding of geometric coverings through analysis of the volume of a generalized difference body.
Contribution
It introduces the first nontrivial lower bound for lattice covering density specifically for n-dimensional simplices, using volume analysis of a generalized difference body.
Findings
First nontrivial lower bound for lattice covering density by simplices
Uses volume of generalized difference body for bounds
Advances geometric covering theory
Abstract
By studying the volume of a generalized difference body, this paper presents the first nontrivial lower bound for the lattice covering density by -dimensional simplices.
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Taxonomy
TopicsGraph theory and applications · graph theory and CDMA systems · Advanced Graph Theory Research