{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/16463"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/16463","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Cliques in block graphs of designs and orthogonal arrays","abstract":"The Erdos-Ko-Rado [EKR] Theorem for intersecting families is a fundamental result in combinatorics, particularly in extremal set theory. This theorem not only establishes an upper bound on the size of the largest intersecting family but also characterizes the families that attain this bound—–these are known as maximal canonically intersecting. Recent work by Balogh, Das, Delcourt, Liu, and Sharifzadeh delves into intersecting families across permutations, hypergraphs, and vector spaces, revealing that nearly all such families within these structures are a subset of a maximal canonically intersecting family [1]. Building on these insights, this thesis extends the examination to block graphs of designs and orthogonal arrays. Through a comprehensive analysis of intersecting families within designs, we introduce a ratio between canonically intersecting families and non-canonical ones, demonstrating that almost all intersecting families in designs are canonical. This method, adaptable to orthogonal arrays OA(m, n) for sufficiently large n, is complemented by a conjecture proposing a second proof inspired by the methods given by Balogh et al. Notably, these results exclude symmetric and affine designs.","abstract_html":"The Erdos-Ko-Rado [EKR] Theorem for intersecting families is a fundamental result in combinatorics, particularly in extremal set theory. This theorem not only establishes an upper bound on the size of the largest intersecting family but also characterizes the families that attain this bound—–these are known as maximal canonically intersecting. Recent work by Balogh, Das, Delcourt, Liu, and Sharifzadeh delves into intersecting families across permutations, hypergraphs, and vector spaces, revealing that nearly all such families within these structures are a subset of a maximal canonically intersecting family [1]. Building on these insights, this thesis extends the examination to block graphs of designs and orthogonal arrays. Through a comprehensive analysis of intersecting families within designs, we introduce a ratio between canonically intersecting families and non-canonical ones, demonstrating that almost all intersecting families in designs are canonical. This method, adaptable to orthogonal arrays OA(m, n) for sufficiently large n, is complemented by a conjecture proposing a second proof inspired by the methods given by Balogh et al. Notably, these results exclude symmetric and affine designs.","abstract_has_math":false,"creators":["Evans, Rachel Anne"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Science (MSc)","degree_level":"Master's","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Meagher, Karen"],"committee_chairs":[],"committee_members":["Kozdron, Michael","Pantangi, Venkata Raghu Tej"],"year":2024,"date_issued":"2024-03","date_published":"2024-03","updated_at":"2026-07-24T04:03:47Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4932"],"render_values":[{"text":"https://doi.org/10.82465/4932","href":"https://doi.org/10.82465/4932","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/16463","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Meagher, Karen"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Kozdron, Michael","Pantangi, Venkata Raghu Tej"]},{"key":"dc:creator","label":"Author","values":["Evans, Rachel Anne"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-10-11T20:00:35Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-10-11T20:00:35Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-03"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"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.doi","label":"DOI","values":["https://doi.org/10.82465/4932"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/16463"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics, University of Regina. ix, 108 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["The Erdos-Ko-Rado [EKR] Theorem for intersecting families is a fundamental result in combinatorics, particularly in extremal set theory. This theorem not only establishes an upper bound on the size of the largest intersecting family but also characterizes the families that attain this bound—–these are known as maximal canonically intersecting. Recent work by Balogh, Das, Delcourt, Liu, and Sharifzadeh delves into intersecting families across permutations, hypergraphs, and vector spaces, revealing that nearly all such families within these structures are a subset of a maximal canonically intersecting family [1]. Building on these insights, this thesis extends the examination to block graphs of designs and orthogonal arrays. Through a comprehensive analysis of intersecting families within designs, we introduce a ratio between canonically intersecting families and non-canonical ones, demonstrating that almost all intersecting families in designs are canonical. This method, adaptable to orthogonal arrays OA(m, n) for sufficiently large n, is complemented by a conjecture proposing a second proof inspired by the methods given by Balogh et al. Notably, these results exclude symmetric and affine designs."]},{"key":"dc:title","label":"Title","values":["Cliques in block graphs of designs and orthogonal arrays"]}]}],"canonical_facts":{"dc:contributor.advisor":["Meagher, Karen"],"dc:contributor.committeemember":["Kozdron, Michael","Pantangi, Venkata Raghu Tej"],"dc:creator":["Evans, Rachel Anne"],"dc:date.accessioned":["2024-10-11T20:00:35Z"],"dc:date.available":["2024-10-11T20:00:35Z"],"dc:date.issued":["2024-03"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics, University of Regina. ix, 108 p."],"dc:description.abstract":["The Erdos-Ko-Rado [EKR] Theorem for intersecting families is a fundamental result in combinatorics, particularly in extremal set theory. This theorem not only establishes an upper bound on the size of the largest intersecting family but also characterizes the families that attain this bound—–these are known as maximal canonically intersecting. Recent work by Balogh, Das, Delcourt, Liu, and Sharifzadeh delves into intersecting families across permutations, hypergraphs, and vector spaces, revealing that nearly all such families within these structures are a subset of a maximal canonically intersecting family [1]. Building on these insights, this thesis extends the examination to block graphs of designs and orthogonal arrays. Through a comprehensive analysis of intersecting families within designs, we introduce a ratio between canonically intersecting families and non-canonical ones, demonstrating that almost all intersecting families in designs are canonical. This method, adaptable to orthogonal arrays OA(m, n) for sufficiently large n, is complemented by a conjecture proposing a second proof inspired by the methods given by Balogh et al. Notably, these results exclude symmetric and affine designs."],"dc:identifier.doi":["https://doi.org/10.82465/4932"],"dc:identifier.uri":["https://hdl.handle.net/10294/16463"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Cliques in block graphs of designs and orthogonal arrays"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:47Z"}