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Author ORCID Identifier
https://orcid.org/0000-0001-9694-0248
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2023
Month Degree Awarded
September
First Advisor
Annie Raymond
Subject Categories
Discrete Mathematics and Combinatorics
Abstract
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.
DOI
https://doi.org/10.7275/35968701
Recommended Citation
Gallagher, Daniel, "FACETS OF THE UNION-CLOSED POLYTOPE" (2023). Doctoral Dissertations. 2884.
https://doi.org/10.7275/35968701
https://scholarworks.umass.edu/dissertations_2/2884
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.