{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86907"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86907","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Minimal Volume K-Point Lattice D-Simplices","abstract":"We begin by showing that minimal volume occurs if and only if the P is a lattice simplex (of dimension d ≠ 2) whose interior lattice points are collinear with a vertex of P. We then show that there can only be one such class of simplices with this property. Interestingly, this statement is not true for d = 2, and counterexamples are provided within.","abstract_html":"We begin by showing that minimal volume occurs if and only if the P is a lattice simplex (of dimension d ≠ 2) whose interior lattice points are collinear with a vertex of P. We then show that there can only be one such class of simplices with this property. Interestingly, this statement is not true for d = 2, and counterexamples are provided within.","abstract_has_math":false,"creators":["Duong, Han"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Reznick, Bruce"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:07Z","date_published":"2015-09-28T15:20:07Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3337777"],"render_values":[{"text":"(MiAaPQ)AAI3337777","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86907","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Reznick, Bruce"]},{"key":"dc:creator","label":"Author","values":["Duong, Han"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:07Z","10000-01-01","2008"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86907","(MiAaPQ)AAI3337777"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We begin by showing that minimal volume occurs if and only if the P is a lattice simplex (of dimension d ≠ 2) whose interior lattice points are collinear with a vertex of P. We then show that there can only be one such class of simplices with this property. Interestingly, this statement is not true for d = 2, and counterexamples are provided within.","Made available in DSpace on 2015-09-28T15:20:07Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3337777.pdf: 711844 bytes, checksum: 51f6a2bcb0fc53dda8d84c5f180ac86b (MD5) Previous issue date: 2008","Embargo set by: Seth Robbins for item 88188 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","47 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008."]},{"key":"dc:title","label":"Title","values":["Minimal Volume K-Point Lattice D-Simplices"]}]}],"canonical_facts":{"dc:contributor":["Reznick, Bruce"],"dc:creator":["Duong, Han"],"dc:date":["2015-09-28T15:20:07Z","10000-01-01","2008"],"dc:description":["We begin by showing that minimal volume occurs if and only if the P is a lattice simplex (of dimension d ≠ 2) whose interior lattice points are collinear with a vertex of P. We then show that there can only be one such class of simplices with this property. Interestingly, this statement is not true for d = 2, and counterexamples are provided within.","Made available in DSpace on 2015-09-28T15:20:07Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3337777.pdf: 711844 bytes, checksum: 51f6a2bcb0fc53dda8d84c5f180ac86b (MD5) Previous issue date: 2008","Embargo set by: Seth Robbins for item 88188 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","47 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008."],"dc:identifier":["http://hdl.handle.net/2142/86907","(MiAaPQ)AAI3337777"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Minimal Volume K-Point Lattice D-Simplices"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}