{"id":{"repo_id":"usf","oai_identifier":"oai:digitalcommons.usf.edu:etd-1198"},"canonical_url":"https://search.dev.ndltd.org/etd/usf/oai:digitalcommons.usf.edu:etd-1198","repository":{"repo_id":"usf","name":"University of South Florida","base_url":"https://digitalcommons.usf.edu/do/oai/"},"display":{"title":"Subconstituent Algebras of Latin Squares","abstract":"Let n be a positive integer. A Latin square of order n is an n×n array L such that each element of some n-set occurs in each row and in each column of L exactly once. It is well-known that one may construct a 4-class association scheme on the positions of a Latin square, where the relations are the identity, being in the same row, being in the same column, having the same entry, and everything else. We describe the subconstituent (Terwilliger) algebras of such an association scheme. One also may construct several strongly regular graphs on the positions of a Latin square, where adjacency corresponds to any subset of the nonidentity relations described above. We describe the local spectrum and subconstituent algebras of such strongly regular graphs. Finally, we study various notions of isomorphism for subconstituent algebras using Latin squares as examples.","abstract_html":"Let n be a positive integer. A Latin square of order n is an n×n array L such that each element of some n-set occurs in each row and in each column of L exactly once. It is well-known that one may construct a 4-class association scheme on the positions of a Latin square, where the relations are the identity, being in the same row, being in the same column, having the same entry, and everything else. We describe the subconstituent (Terwilliger) algebras of such an association scheme. One also may construct several strongly regular graphs on the positions of a Latin square, where adjacency corresponds to any subset of the nonidentity relations described above. We describe the local spectrum and subconstituent algebras of such strongly regular graphs. Finally, we study various notions of isomorphism for subconstituent algebras using Latin squares as examples.","abstract_has_math":false,"creators":["Daqqa, Ibtisam"],"institution":"Digital Commons @ University of South Florida","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2007,"date_issued":"2007-11-29T08:00:00Z","date_published":"2007-11-29T08:00:00Z","updated_at":"2026-07-24T05:42:11Z","subjects":["Terwilliger algebra","Bose-Mesner algebra","Association scheme","Strongly regular graph","Fusions","American Studies","Arts and Humanities"],"languages":[],"rights":["default"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.usf.edu/etd/199","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Daqqa, Ibtisam"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-11-29T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Digital Commons @ University of South Florida"]},{"key":"dc:type","label":"Dc Type","values":["dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Terwilliger algebra","Bose-Mesner algebra","Association scheme","Strongly regular graph","Fusions","American Studies","Arts and Humanities"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["default"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.usf.edu/etd/199","https://digitalcommons.usf.edu/context/etd/article/1198/viewcontent/etd__199.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let n be a positive integer. A Latin square of order n is an n×n array L such that each element of some n-set occurs in each row and in each column of L exactly once. It is well-known that one may construct a 4-class association scheme on the positions of a Latin square, where the relations are the identity, being in the same row, being in the same column, having the same entry, and everything else. We describe the subconstituent (Terwilliger) algebras of such an association scheme. One also may construct several strongly regular graphs on the positions of a Latin square, where adjacency corresponds to any subset of the nonidentity relations described above. We describe the local spectrum and subconstituent algebras of such strongly regular graphs. Finally, we study various notions of isomorphism for subconstituent algebras using Latin squares as examples."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:source","label":"Dc Source","values":["USF Tampa Graduate Theses and Dissertations"]},{"key":"dc:title","label":"Title","values":["Subconstituent Algebras of Latin Squares"]}]}],"canonical_facts":{"dc:creator":["Daqqa, Ibtisam"],"dc:date":["2007-11-29T08:00:00Z"],"dc:description":["Let n be a positive integer. A Latin square of order n is an n×n array L such that each element of some n-set occurs in each row and in each column of L exactly once. It is well-known that one may construct a 4-class association scheme on the positions of a Latin square, where the relations are the identity, being in the same row, being in the same column, having the same entry, and everything else. We describe the subconstituent (Terwilliger) algebras of such an association scheme. One also may construct several strongly regular graphs on the positions of a Latin square, where adjacency corresponds to any subset of the nonidentity relations described above. We describe the local spectrum and subconstituent algebras of such strongly regular graphs. Finally, we study various notions of isomorphism for subconstituent algebras using Latin squares as examples."],"dc:format":["application/pdf"],"dc:identifier":["https://digitalcommons.usf.edu/etd/199","https://digitalcommons.usf.edu/context/etd/article/1198/viewcontent/etd__199.pdf"],"dc:publisher":["Digital Commons @ University of South Florida"],"dc:rights":["default"],"dc:source":["USF Tampa Graduate Theses and Dissertations"],"dc:subject":["Terwilliger algebra","Bose-Mesner algebra","Association scheme","Strongly regular graph","Fusions","American Studies","Arts and Humanities"],"dc:title":["Subconstituent Algebras of Latin Squares"],"dc:type":["dissertation"]},"updated_at":"2026-07-24T05:42:11Z"}