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DOI

https://doi.org/10.25772/GMNF-J690

Defense Date

2023

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematical Sciences

First Advisor

Craig Larson

Abstract

The most common statement of Frankl's conjecture is that for every finite family of sets closed under the union operation, there is some element which belongs to at least half of the sets in the family. Despite its apparent simplicity, Frankl's conjecture has remained open and highly researched since its first mention in 1979. In this paper, we begin by examining the history and previous attempts at solving the conjecture. Using these previous ideas, we introduce the concepts of minimal sets and minimally-generated families, some ideas related to viewing union-closed families as posets, and some constructions of families involving poset-defined parameters such as height and width.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

12-15-2023

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