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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Kogan, David Booth"],"institution":null,"degree_name":"Mathematics, PhD","degree_level":"Open Access Dissertation","degree_discipline":"Institute of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Stephan Ramon Garcia","Allon Percus"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-01-01T08:00:00Z","date_published":"2022-01-01T08:00:00Z","updated_at":"2026-07-24T01:40:15Z","subjects":["coherence","cyclic","cyclotomic","lattice","orthogonal","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarship.claremont.edu/cgu_etd/474","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stephan Ramon Garcia","Allon Percus"]},{"key":"dc:creator","label":"Author","values":["Kogan, David Booth"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2023-04-19T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Institute of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics, PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["coherence","cyclic","cyclotomic","lattice","orthogonal","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarship.claremont.edu/cgu_etd/474"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["On Coherence and the Geometry of Certain Families of Lattices"]}]}],"canonical_facts":{"dc:contributor":["Stephan Ramon Garcia","Allon Percus"],"dc:creator":["Kogan, David Booth"],"dc:date.available":["2023-04-19T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://scholarship.claremont.edu/cgu_etd/474"],"dc:subject":["coherence","cyclic","cyclotomic","lattice","orthogonal","Mathematics"],"dc:title":["On Coherence and the Geometry of Certain Families of Lattices"],"thesis:degree_discipline":["Institute of Mathematical Sciences"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Mathematics, PhD"]},"updated_at":"2026-07-24T01:40:15Z"}