## Theses and Dissertations

#### Title

Multilattice Tilings and Coverings

#### Abstract

Let L be a discrete subgroup of \mathbb{R}^n under addition. Let D be a finite set of points including the origin. These two sets will define a multilattice of \mathbb{R}^n. We explore how to generate a periodic covering of the space \mathbb{R}^n based on L and $D$. Additionally, we explore the problem of covering when we restrict ourselves to covering \mathbb{R}^n using only dilations of the right regular simplex in our covering. We show that using a set D= {0,d} to define our multilattice the minimum covering density is 5-\sqrt{13}. Furthermore, we show that when we allow for an arbitrary number of displacements, we may get arbitrarily close to a covering density of 1.

MS

#### College and Department

Physical and Mathematical Sciences; Mathematics

2021-04-02

Thesis

#### Handle

http://hdl.lib.byu.edu/1877/etd11551

#### Keywords

Multilattice, Covering, Density, Word-length, Simplex

english

COinS