{"id":{"repo_id":"unlv","oai_identifier":"oai:oasis.library.unlv.edu:rtds-2213"},"canonical_url":"https://search.dev.ndltd.org/etd/unlv/oai:oasis.library.unlv.edu:rtds-2213","repository":{"repo_id":"unlv","name":"University of Nevada - Las Vegas","base_url":"https://oasis.library.unlv.edu/do/oai/"},"display":{"title":"Average Cayley genus for Cayley maps with dihedral groups","abstract":"Let Gamma be a finite group and let Delta be a generating set for Gamma. A Cayley map associated with Gamma and Delta is an oriented 2-cell embedding of the Cayley graph GDelta (Gamma) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of generators and their inverses. A formula for the average Cayley genus is known for the dihedral group with generating set consisting of all the reflections. However, the known formula involves sums of certain coefficients of a generating function and its format does not specifically indicate the Cayley genus distribution. We determine a simplified formula for this average Cayley genus as well as provide improved understanding of the Cayley genus distribution.","abstract_html":"Let Gamma be a finite group and let Delta be a generating set for Gamma. A Cayley map associated with Gamma and Delta is an oriented 2-cell embedding of the Cayley graph GDelta (Gamma) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of generators and their inverses. A formula for the average Cayley genus is known for the dihedral group with generating set consisting of all the reflections. However, the known formula involves sums of certain coefficients of a generating function and its format does not specifically indicate the Cayley genus distribution. We determine a simplified formula for this average Cayley genus as well as provide improved understanding of the Cayley genus distribution.","abstract_has_math":false,"creators":["Langille, Jamie Keith"],"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":["Michelle Schultz"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2000,"date_issued":"2000-01-01T08:00:00Z","date_published":"2000-01-01T08:00:00Z","updated_at":"2026-07-24T05:25:18Z","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/1214"],"render_values":[{"text":"https://oasis.library.unlv.edu/rtds/1214","href":"https://oasis.library.unlv.edu/rtds/1214","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.25669/ezxp-f1u0","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Michelle Schultz"]},{"key":"dc:creator","label":"Author","values":["Langille, Jamie Keith"]}]},{"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. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.25669/ezxp-f1u0","https://oasis.library.unlv.edu/rtds/1214","https://oasis.library.unlv.edu/context/rtds/article/2213/viewcontent/uc.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let Gamma be a finite group and let Delta be a generating set for Gamma. A Cayley map associated with Gamma and Delta is an oriented 2-cell embedding of the Cayley graph GDelta (Gamma) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of generators and their inverses. A formula for the average Cayley genus is known for the dihedral group with generating set consisting of all the reflections. However, the known formula involves sums of certain coefficients of a generating function and its format does not specifically indicate the Cayley genus distribution. We determine a simplified formula for this average Cayley genus as well as provide improved understanding of the Cayley genus distribution."]},{"key":"dc:format","label":"Dc Format","values":["pdf"]},{"key":"dc:title","label":"Title","values":["Average Cayley genus for Cayley maps with dihedral groups"]}]}],"canonical_facts":{"dc:contributor":["Michelle Schultz"],"dc:creator":["Langille, Jamie Keith"],"dc:description.abstract":["Let Gamma be a finite group and let Delta be a generating set for Gamma. A Cayley map associated with Gamma and Delta is an oriented 2-cell embedding of the Cayley graph GDelta (Gamma) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of generators and their inverses. A formula for the average Cayley genus is known for the dihedral group with generating set consisting of all the reflections. However, the known formula involves sums of certain coefficients of a generating function and its format does not specifically indicate the Cayley genus distribution. We determine a simplified formula for this average Cayley genus as well as provide improved understanding of the Cayley genus distribution."],"dc:format":["pdf"],"dc:identifier":["10.25669/ezxp-f1u0","https://oasis.library.unlv.edu/rtds/1214","https://oasis.library.unlv.edu/context/rtds/article/2213/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":["Average Cayley genus for Cayley maps with dihedral groups"],"dc:type":["Text"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:25:18Z"}