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Author ORCID Identifier
Open Access Dissertation
Doctor of Philosophy (PhD)
Year Degree Awarded
Month Degree Awarded
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.
Gallagher, Daniel, "FACETS OF THE UNION-CLOSED POLYTOPE" (2023). Doctoral Dissertations. 2884.
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