On Coherence and the Geometry of Certain Families of Lattices

<p>The coherence of a lattice is, roughly speaking, a measure of non-orthogonality of its minimal vectors. It was introduced to lattices (by analogy with frame theory) by L. Fukshansky and others as a possible route to gaining insight into packing density, a central problem in lattice theory. In this work, we introduce the related measure of average coherence, explore connections between packing density and coherence, and prove several properties of certain families of lattices, most notably nearly orthogonal lattices, cyclotomic lattices, and cyclic lattices.</p>

Name thesis:degree_name

Mathematics, PhD

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Institute of Mathematical Sciences

Year dc:date.available

2022

Author dc:creator

• Kogan, David Booth

Contributors dc:contributor

• Stephan Ramon Garcia
• Allon Percus

• coherence
• cyclic
• cyclotomic
• lattice
• orthogonal
• Mathematics

Repository record dc:identifier

https://scholarship.claremont.edu/cgu_etd/474

OAI identifier oai:identifier

oai:scholarship.claremont.edu:cgu_etd-1505