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Author ORCID Identifier


Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Annie Raymond

Subject Categories

Discrete Mathematics and Combinatorics


In 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.


Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.