{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/59323"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/59323","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Divisibility Conditions for Fibonomial Coefficients","abstract":"The fibonomial triangle has been shown by Chen and Sagan to have a fractal nature mod 2 and 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, showing with a theorem of Knuth and Wilf that the triangle has a recurring structure under divisibility by five. While this result is not new, our method of proof is new and suggests a theorem relating the divisibility by a general prime $p$ of a fibonomial coefficient to the divisibility by $p$ of a product of fibonomial coefficients in the first $p$ rows of the fibonomial triangle. This product is constructed using a particular base. We give necessary and sufficient conditions for which primes $p$ satisfy the theorem, namely that the Fibonacci entry point of $p$ must be greater than or equal to $p$ for the theorem to hold. Lastly, we conclude with a discussion concerning further directions of research.","abstract_html":"The fibonomial triangle has been shown by Chen and Sagan to have a fractal nature mod 2 and 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, showing with a theorem of Knuth and Wilf that the triangle has a recurring structure under divisibility by five. While this result is not new, our method of proof is new and suggests a theorem relating the divisibility by a general prime $p$ of a fibonomial coefficient to the divisibility by $p$ of a product of fibonomial coefficients in the first $p$ rows of the fibonomial triangle. This product is constructed using a particular base. We give necessary and sufficient conditions for which primes $p$ satisfy the theorem, namely that the Fibonacci entry point of $p$ must be greater than or equal to $p$ for the theorem to hold. Lastly, we conclude with a discussion concerning further directions of research.","abstract_has_math":true,"creators":["Southwick, Jeremiah T."],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-27T22:02:05Z","subjects":["Fibonomial"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/59323","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Southwick, Jeremiah T."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-05-21T08:35:53Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-21T08:35:53Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Fibonomial"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/59323"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The fibonomial triangle has been shown by Chen and Sagan to have a fractal nature mod 2 and 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, showing with a theorem of Knuth and Wilf that the triangle has a recurring structure under divisibility by five. While this result is not new, our method of proof is new and suggests a theorem relating the divisibility by a general prime $p$ of a fibonomial coefficient to the divisibility by $p$ of a product of fibonomial coefficients in the first $p$ rows of the fibonomial triangle. This product is constructed using a particular base. We give necessary and sufficient conditions for which primes $p$ satisfy the theorem, namely that the Fibonacci entry point of $p$ must be greater than or equal to $p$ for the theorem to hold. Lastly, we conclude with a discussion concerning further directions of research."]},{"key":"dc:title","label":"Title","values":["Divisibility Conditions for Fibonomial Coefficients"]}]}],"canonical_facts":{"dc:creator":["Southwick, Jeremiah T."],"dc:date.accessioned":["2016-05-21T08:35:53Z"],"dc:date.available":["2016-05-21T08:35:53Z"],"dc:date.issued":["2016"],"dc:description.abstract":["The fibonomial triangle has been shown by Chen and Sagan to have a fractal nature mod 2 and 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, showing with a theorem of Knuth and Wilf that the triangle has a recurring structure under divisibility by five. While this result is not new, our method of proof is new and suggests a theorem relating the divisibility by a general prime $p$ of a fibonomial coefficient to the divisibility by $p$ of a product of fibonomial coefficients in the first $p$ rows of the fibonomial triangle. This product is constructed using a particular base. We give necessary and sufficient conditions for which primes $p$ satisfy the theorem, namely that the Fibonacci entry point of $p$ must be greater than or equal to $p$ for the theorem to hold. Lastly, we conclude with a discussion concerning further directions of research."],"dc:identifier.uri":["http://hdl.handle.net/10339/59323"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["Fibonomial"],"dc:title":["Divisibility Conditions for Fibonomial Coefficients"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:02:05Z"}