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FACETS OF THE UNION-CLOSED POLYTOPE

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dc.contributor.advisorAnnie Raymond
dc.contributor.authorGallagher, Daniel
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2024-03-27T18:49:37.000
dc.date.accessioned2024-04-26T16:01:39Z
dc.date.available2024-04-26T16:01:39Z
dc.date.submittedSeptember
dc.date.submitted2023
dc.description.abstractIn the haze of the 1970s, a conjecture was born to unknown parentage...the union-closed sets conjecture. Given a family of sets $\FF$, we say that $\FF$ is union-closed if for every two sets $S, T \in \FF$, we have $S \cup T \in \FF$. The union-closed sets conjecture states that there is an element in at least half of the sets of any (non-empty) union-closed family. In 2016, Pulaj, Raymond, and Theis reinterpreted the conjecture as an optimization problem that could be formulated as an integer program. This thesis is concerned with the study of the polytope formed by taking the convex hull of the integer points satisfying the integer program. We find several facets and describe some small cases of this complicated polytope in full.
dc.description.degreeDoctor of Philosophy (PhD)
dc.description.departmentMathematics
dc.identifier.doihttps://doi.org/10.7275/35968701
dc.identifier.orcidhttps://orcid.org/0000-0001-9694-0248
dc.identifier.urihttps://hdl.handle.net/20.500.14394/19262
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=4051&context=dissertations_2&unstamped=1
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.source.statuspublished
dc.subjectCombinatorics
dc.subjectdiscrete math
dc.subjectunion-closed
dc.subjectFrankl
dc.subjectDiscrete Mathematics and Combinatorics
dc.titleFACETS OF THE UNION-CLOSED POLYTOPE
dc.typeopenaccess
dc.typearticle
dc.typedissertation
digcom.contributor.authorisAuthorOfPublication|email:dgallagher@umass.edu|institution:University of Massachusetts Amherst|Gallagher, Daniel
digcom.identifierdissertations_2/2884
digcom.identifier.contextkey35968701
digcom.identifier.submissionpathdissertations_2/2884
dspace.entity.typePublication
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