{"id":{"repo_id":"unlv","oai_identifier":"oai:oasis.library.unlv.edu:rtds-2417"},"canonical_url":"https://search.dev.ndltd.org/etd/unlv/oai:oasis.library.unlv.edu:rtds-2417","repository":{"repo_id":"unlv","name":"University of Nevada - Las Vegas","base_url":"https://oasis.library.unlv.edu/do/oai/"},"display":{"title":"Representation of special polynomials by the cycle indicator","abstract":"Certain classes of special functions have been shown to have Cycle Indicator representations as well as recurrence relations. Most remarkably, it is shown how the Cycle Indicator can be used to unify or generalize special functions. Methods of unifying special functions are elaborated on. It follows that classical special functions with simple logarithms of their generating functions can be classified in this way. Also, there are counter-examples where the Cycle Indicator doesn't represent the special functions given; This thesis represents a study of a journal article called \"Cycle Indicators and Special Functions\" by Leetsch C. Hsu and Peter Jau-Shyong Shiue in the Annals of Combinatorics (cf. Hsu and Shiue, [10]).","abstract_html":"Certain classes of special functions have been shown to have Cycle Indicator representations as well as recurrence relations. Most remarkably, it is shown how the Cycle Indicator can be used to unify or generalize special functions. Methods of unifying special functions are elaborated on. It follows that classical special functions with simple logarithms of their generating functions can be classified in this way. Also, there are counter-examples where the Cycle Indicator doesn't represent the special functions given; This thesis represents a study of a journal article called "Cycle Indicators and Special Functions" by Leetsch C. Hsu and Peter Jau-Shyong Shiue in the Annals of Combinatorics (cf. Hsu and Shiue, [10]).","abstract_has_math":false,"creators":["Schofield, Jack Lund"],"institution":"University of Nevada, Las Vegas","degree_name":"Master of Science (MS)","degree_level":"Thesis","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Peter Shiue"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2002,"date_issued":"2002-01-01T08:00:00Z","date_published":"2002-01-01T08:00:00Z","updated_at":"2026-07-24T05:25:26Z","subjects":[],"languages":["English"],"rights":["IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://oasis.library.unlv.edu/rtds/1418"],"render_values":[{"text":"https://oasis.library.unlv.edu/rtds/1418","href":"https://oasis.library.unlv.edu/rtds/1418","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.25669/ylvn-z87y","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Peter Shiue"]},{"key":"dc:creator","label":"Author","values":["Schofield, Jack Lund"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["University of Nevada, Las Vegas"]},{"key":"dc:type","label":"Dc Type","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["IN COPYRIGHT. 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Also, there are counter-examples where the Cycle Indicator doesn't represent the special functions given; This thesis represents a study of a journal article called \"Cycle Indicators and Special Functions\" by Leetsch C. Hsu and Peter Jau-Shyong Shiue in the Annals of Combinatorics (cf. Hsu and Shiue, [10])."]},{"key":"dc:format","label":"Dc Format","values":["pdf"]},{"key":"dc:title","label":"Title","values":["Representation of special polynomials by the cycle indicator"]}]}],"canonical_facts":{"dc:contributor":["Peter Shiue"],"dc:creator":["Schofield, Jack Lund"],"dc:description.abstract":["Certain classes of special functions have been shown to have Cycle Indicator representations as well as recurrence relations. Most remarkably, it is shown how the Cycle Indicator can be used to unify or generalize special functions. Methods of unifying special functions are elaborated on. It follows that classical special functions with simple logarithms of their generating functions can be classified in this way. Also, there are counter-examples where the Cycle Indicator doesn't represent the special functions given; This thesis represents a study of a journal article called \"Cycle Indicators and Special Functions\" by Leetsch C. Hsu and Peter Jau-Shyong Shiue in the Annals of Combinatorics (cf. Hsu and Shiue, [10])."],"dc:format":["pdf"],"dc:identifier":["10.25669/ylvn-z87y","https://oasis.library.unlv.edu/rtds/1418","https://oasis.library.unlv.edu/context/rtds/article/2417/viewcontent/uc.pdf"],"dc:language":["English"],"dc:publisher":["University of Nevada, Las Vegas"],"dc:rights":["IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Representation of special polynomials by the cycle indicator"],"dc:type":["Text"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:25:26Z"}