{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/14360"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/14360","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Cameron-Liebler Sets for 2-Transitive Groups","abstract":"This research was conducted on 2-transitive groups whose minimal normal subgroup is abelian. Suppose G is such a group and ΓG is its derangement graph. Any maximum coclique S of ΓG has a characteristic vector xS. Each xS is a boolean vector contained in a particular module, which is called the permutation module MP. This module has a dimension of 1 + (n − 1)2, where n = deg(G), and it is spanned by {xij | i,j∈{1,...,n}}, where each xij is the characteristic vector of Sij, the set of permutations that map i to j. Apart from the xij, which correspond to the stabilizers of G and their cosets, this research set out to find any other boolean vectors that are contained in Mp using linear programming. Henceforth, such boolean vectors are defined to be Cameron-Liebler sets for 2-transitive groups. In addition to finding Cameron-Liebler sets, analyses were performed on each group to determine: (1) whether the strict EKR property holds; (2) the number of maximum cocliques that are subgroups, cosets, or neither; (3) isomorphism classes and conjugacy classes of the maximum cocliques that are subgroups; (4) the dimension of C′, the maximum cliques that are subgroups (along with their right cosets), and C, all maximum cliques; and (5) the spectrum of ΓG and whether the ratio bound is satisfied with equality.","abstract_html":"This research was conducted on 2-transitive groups whose minimal normal subgroup is abelian. Suppose G is such a group and ΓG is its derangement graph. Any maximum coclique S of ΓG has a characteristic vector xS. Each xS is a boolean vector contained in a particular module, which is called the permutation module MP. This module has a dimension of 1 + (n − 1)2, where n = deg(G), and it is spanned by {xij | i,j∈{1,...,n}}, where each xij is the characteristic vector of Sij, the set of permutations that map i to j. Apart from the xij, which correspond to the stabilizers of G and their cosets, this research set out to find any other boolean vectors that are contained in Mp using linear programming. Henceforth, such boolean vectors are defined to be Cameron-Liebler sets for 2-transitive groups. In addition to finding Cameron-Liebler sets, analyses were performed on each group to determine: (1) whether the strict EKR property holds; (2) the number of maximum cocliques that are subgroups, cosets, or neither; (3) isomorphism classes and conjugacy classes of the maximum cocliques that are subgroups; (4) the dimension of C′, the maximum cliques that are subgroups (along with their right cosets), and C, all maximum cliques; and (5) the spectrum of ΓG and whether the ratio bound is satisfied with equality.","abstract_has_math":false,"creators":["Palmarin, Daniel Michael"],"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":["Fallat, Shaun","Meagher, Karen"],"committee_chairs":[],"committee_members":["Herman, Allen"],"year":2020,"date_issued":"2020-11","date_published":"2020-11","updated_at":"2026-07-24T04:03:43Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4707"],"render_values":[{"text":"https://doi.org/10.82465/4707","href":"https://doi.org/10.82465/4707","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/14360","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Fallat, Shaun","Meagher, Karen"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Herman, Allen"]},{"key":"dc:creator","label":"Author","values":["Palmarin, Daniel Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-09-22T22:25:23Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-09-22T22:25:23Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-11"]},{"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/10.82465/4707"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/14360"]}]},{"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. xii, 118 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["This research was conducted on 2-transitive groups whose minimal normal subgroup is abelian. Suppose G is such a group and ΓG is its derangement graph. Any maximum coclique S of ΓG has a characteristic vector xS. Each xS is a boolean vector contained in a particular module, which is called the permutation module MP. This module has a dimension of 1 + (n − 1)2, where n = deg(G), and it is spanned by {xij | i,j∈{1,...,n}}, where each xij is the characteristic vector of Sij, the set of permutations that map i to j. Apart from the xij, which correspond to the stabilizers of G and their cosets, this research set out to find any other boolean vectors that are contained in Mp using linear programming. Henceforth, such boolean vectors are defined to be Cameron-Liebler sets for 2-transitive groups. In addition to finding Cameron-Liebler sets, analyses were performed on each group to determine: (1) whether the strict EKR property holds; (2) the number of maximum cocliques that are subgroups, cosets, or neither; (3) isomorphism classes and conjugacy classes of the maximum cocliques that are subgroups; (4) the dimension of C′, the maximum cliques that are subgroups (along with their right cosets), and C, all maximum cliques; and (5) the spectrum of ΓG and whether the ratio bound is satisfied with equality."]},{"key":"dc:title","label":"Title","values":["Cameron-Liebler Sets for 2-Transitive Groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Fallat, Shaun","Meagher, Karen"],"dc:contributor.committeemember":["Herman, Allen"],"dc:creator":["Palmarin, Daniel Michael"],"dc:date.accessioned":["2021-09-22T22:25:23Z"],"dc:date.available":["2021-09-22T22:25:23Z"],"dc:date.issued":["2020-11"],"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. xii, 118 p."],"dc:description.abstract":["This research was conducted on 2-transitive groups whose minimal normal subgroup is abelian. Suppose G is such a group and ΓG is its derangement graph. Any maximum coclique S of ΓG has a characteristic vector xS. Each xS is a boolean vector contained in a particular module, which is called the permutation module MP. This module has a dimension of 1 + (n − 1)2, where n = deg(G), and it is spanned by {xij | i,j∈{1,...,n}}, where each xij is the characteristic vector of Sij, the set of permutations that map i to j. Apart from the xij, which correspond to the stabilizers of G and their cosets, this research set out to find any other boolean vectors that are contained in Mp using linear programming. Henceforth, such boolean vectors are defined to be Cameron-Liebler sets for 2-transitive groups. In addition to finding Cameron-Liebler sets, analyses were performed on each group to determine: (1) whether the strict EKR property holds; (2) the number of maximum cocliques that are subgroups, cosets, or neither; (3) isomorphism classes and conjugacy classes of the maximum cocliques that are subgroups; (4) the dimension of C′, the maximum cliques that are subgroups (along with their right cosets), and C, all maximum cliques; and (5) the spectrum of ΓG and whether the ratio bound is satisfied with equality."],"dc:identifier.doi":["https://doi.org/10.82465/4707"],"dc:identifier.uri":["https://hdl.handle.net/10294/14360"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Cameron-Liebler Sets for 2-Transitive Groups"],"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":"2026-07-24T04:03:43Z"}