A matroid M is a finite set E, called the ground set of M, together with a notion of what it means for subsets of E to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important property that was very useful in the recent proof of Rota's conjecture, which remained an unsolved problem for 40 years in matroid theory. In this thesis, we give a characterization of regular round matroids.
","abstract_html":"<p>A matroid <em>M</em> is a finite set <em>E</em>, called the ground set of <em>M</em>, together with a notion of what it means for subsets of <em>E</em> to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important property that was very useful in the recent proof of Rota's conjecture, which remained an unsolved problem for 40 years in matroid theory. In this thesis, we give a characterization of regular round matroids.</p>","abstract_has_math":false,"creators":["Borissova, Svetlana"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Aikin, Jeremy"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-12-01T08:00:00Z","date_published":"2016-12-01T08:00:00Z","updated_at":"2026-07-24T01:53:07Z","subjects":["matroid","regular","round","graphic","cographic","decomposition","Other Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/423","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Aikin, Jeremy"]},{"key":"dc:creator","label":"Author","values":["Borissova, Svetlana"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-11-09T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["matroid","regular","round","graphic","cographic","decomposition","Other Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/423"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A matroid M is a finite set E, called the ground set of M, together with a notion of what it means for subsets of E to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important property that was very useful in the recent proof of Rota's conjecture, which remained an unsolved problem for 40 years in matroid theory. In this thesis, we give a characterization of regular round matroids.
"]},{"key":"dc:title","label":"Title","values":["Regular Round Matroids"]}]}],"canonical_facts":{"dc:contributor":["Aikin, Jeremy"],"dc:creator":["Borissova, Svetlana"],"dc:date.available":["2016-11-09T08:00:00Z"],"dc:description.abstract":["A matroid M is a finite set E, called the ground set of M, together with a notion of what it means for subsets of E to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important property that was very useful in the recent proof of Rota's conjecture, which remained an unsolved problem for 40 years in matroid theory. In this thesis, we give a characterization of regular round matroids.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/423"],"dc:subject":["matroid","regular","round","graphic","cographic","decomposition","Other Mathematics"],"dc:title":["Regular Round Matroids"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:53:07Z"}