Date of Award
Fall 2022
Degree Type
Open Access Dissertation
Degree Name
Mathematics, PhD
Program
Institute of Mathematical Sciences
Advisor/Supervisor/Committee Chair
Lenny Fukshansky
Dissertation or Thesis Committee Member
Stephan Ramon Garcia
Dissertation or Thesis Committee Member
Allon Percus
Terms of Use & License Information
Rights Information
© 2022 David B Kogan
Keywords
coherence, cyclic, cyclotomic, lattice, orthogonal
Subject Categories
Mathematics
Abstract
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.
ISBN
9798351417707
Recommended Citation
Kogan, David Booth. (2022). On Coherence and the Geometry of Certain Families of Lattices. CGU Theses & Dissertations, 474. https://scholarship.claremont.edu/cgu_etd/474.
