{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-1456"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-1456","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"On the Combinatorics of Certain Garside Semigroups","abstract":"In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups.","abstract_html":"In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups.","abstract_has_math":false,"creators":["Cornwell, Christopher R."],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:27:55Z","subjects":["mathematics","geometric group theory","braid groups","Garside groups","combinatorics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/457","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Cornwell, Christopher R."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2006-07-06T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["mathematics","geometric group theory","braid groups","Garside groups","combinatorics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/457","https://scholarsarchive.byu.edu/context/etd/article/1456/viewcontent/ETD_CISOPTR_677.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["On the Combinatorics of Certain Garside Semigroups"]}]}],"canonical_facts":{"dc:creator":["Cornwell, Christopher R."],"dc:date":["2006-07-06T07:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Mathematics"],"dc:description.abstract":["In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/457","https://scholarsarchive.byu.edu/context/etd/article/1456/viewcontent/ETD_CISOPTR_677.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["mathematics","geometric group theory","braid groups","Garside groups","combinatorics"],"dc:title":["On the Combinatorics of Certain Garside Semigroups"],"dc:type":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:27:55Z"}