{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/50750"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/50750","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Density and spacing properties of some families of non-standard ternary representations","abstract":"In this dissertation, we study a family of non-standard digital representations in base 3. Let A be an index set such that A={0,u1,u2}, where u1 is equivalent to 1 (mod 3) and u2 is equivalent to 2 (mod 3). We study the set of integers which can be written as \\sum_{i=0}^{\\infty}\\epsilon_i 3^i, where \\epsilon_i is in A. Most of the work in this dissertation is about the case that the index set A={0,1,5}. We are particularly interested in the maximal sets of consecutive integers, the density of the represented numbers and the related generating functions.","abstract_html":"In this dissertation, we study a family of non-standard digital representations in base 3. Let A be an index set such that A={0,u1,u2}, where u1 is equivalent to 1 (mod 3) and u2 is equivalent to 2 (mod 3). We study the set of integers which can be written as \\sum_{i=0}^{\\infty}\\epsilon_i 3^i, where \\epsilon_i is in A. Most of the work in this dissertation is about the case that the index set A={0,1,5}. We are particularly interested in the maximal sets of consecutive integers, the density of the represented numbers and the related generating functions.","abstract_has_math":false,"creators":["Tangjai, Wipawee"],"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 A.","Hildebrand, A.J.","Boca, Florin","Ahlgren, Scott"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-09-16T17:26:10Z","date_published":"2014-09-16T17:26:10Z","updated_at":"2026-07-22T22:25:41Z","subjects":["Combinatorial number theory","Digital representation","non-standard digit sets","ternary representations","generating functions","sequences","subsets of integers"],"languages":["en"],"rights":["Copyright 2014 Wipawee Tangjai"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/50750","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Reznick, Bruce A.","Hildebrand, A.J.","Boca, Florin","Ahlgren, Scott"]},{"key":"dc:creator","label":"Author","values":["Tangjai, Wipawee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-09-16T17:26:10Z","2014-08","2014-09-16"]},{"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":["Combinatorial number theory","Digital representation","non-standard digit sets","ternary representations","generating functions","sequences","subsets of integers"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Wipawee Tangjai"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/50750"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this dissertation, we study a family of non-standard digital representations in base 3. 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