{"id":{"repo_id":"unt","oai_identifier":"info:ark/67531/metadc3676"},"canonical_url":"https://search.dev.ndltd.org/etd/unt/info:ark/67531/metadc3676","repository":{"repo_id":"unt","name":"University of North Texas","base_url":"https://digital.library.unt.edu/oai/"},"display":{"title":"Around the Fibonacci Numeration System","abstract":"Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.","abstract_html":"Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.","abstract_has_math":false,"creators":["Edson, Marcia Ruth"],"institution":"University of North Texas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Zamboni, Luca","Cherry, William, 1966-","Richter, Olav"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2007,"date_issued":"2007-05","date_published":"2007-05","updated_at":"2026-07-24T05:34:52Z","subjects":["numeration systems","positive integer","Fibonacci sequence","Fibonacci numbers.","Fine and Wilf theorem","general and Euclidian algorithms"],"languages":["English"],"rights":["Public","Copyright","Edson, Marcia Ruth","Copyright is held by the author, unless otherwise noted. All rights reserved."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["oclc: 179921850","https://digital.library.unt.edu/ark:/67531/metadc3676/","ark: ark:/67531/metadc3676"],"render_values":[{"text":"oclc: 179921850","href":null,"code":true},{"text":"https://digital.library.unt.edu/ark:/67531/metadc3676/","href":"https://digital.library.unt.edu/ark:/67531/metadc3676/","code":true},{"text":"ark: ark:/67531/metadc3676","href":null,"code":true}]}]},"links":{"outbound_url":"https://doi.org/10.12794/metadc3676","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Zamboni, Luca","Cherry, William, 1966-","Richter, Olav"]},{"key":"dc:creator","label":"Author","values":["Edson, Marcia Ruth"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-05"]},{"key":"dc:publisher","label":"Institution","values":["University of North Texas"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["numeration systems","positive integer","Fibonacci sequence","Fibonacci numbers.","Fine and Wilf theorem","general and Euclidian algorithms"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["Public","Copyright","Edson, Marcia Ruth","Copyright is held by the author, unless otherwise noted. 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In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two."]},{"key":"dc:format","label":"Dc Format","values":["Text"]},{"key":"dc:title","label":"Title","values":["Around the Fibonacci Numeration System"]}]}],"canonical_facts":{"dc:contributor":["Zamboni, Luca","Cherry, William, 1966-","Richter, Olav"],"dc:creator":["Edson, Marcia Ruth"],"dc:date":["2007-05"],"dc:description":["Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two."],"dc:format":["Text"],"dc:identifier":["oclc: 179921850","doi: 10.12794/metadc3676","https://digital.library.unt.edu/ark:/67531/metadc3676/","ark: ark:/67531/metadc3676"],"dc:language":["English"],"dc:publisher":["University of North Texas"],"dc:rights":["Public","Copyright","Edson, Marcia Ruth","Copyright is held by the author, unless otherwise noted. All rights reserved."],"dc:subject":["numeration systems","positive integer","Fibonacci sequence","Fibonacci numbers.","Fine and Wilf theorem","general and Euclidian algorithms"],"dc:title":["Around the Fibonacci Numeration System"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:34:52Z"}