Open Access Honors Program Thesis
Adrienne Stanley, Honors Thesis Advisor
Data sets; Combinatorial set theory;
Mathematicians are often intrigued with patterns, many times finding themselves looking for pieces of structure within a data set. This research project is no different in that we have explored our vast data set for substructure.
Our goal is to identify the following: how many data points are necessary to guarantee our set has a balanced set/substructure? Naturally rephrasing the previous question, we also ask ourselves what is the largest set that does not have a balanced subset/substructure? This alternate phrasing set us down our current path. We focused on the largest sets with no balanced substructure and what they look like.
After brute force checking all Z5 × Z5 maximal sets, we found 7 nonisomorphic graphs that did not have balanced substructure. Using those examples as starting points, we then extended into Z7 × Z7. When successful, our goal was to classify examples in Zp × Zp which have no balanced substructure.
Currently, we believe there are four classifications of maximal sets with no balance substructure for any Zp × Zp. The main proof to follow focuses on one of these classifications called Kick It
Year of Submission
Department of Mathematics
University Honors Designation
A thesis submitted in partial fulfillment of the requirements for the designation University Honors
1 PDF file (23 pages)
©2018 Jake Allen Weber
Weber, Jake Allen, "Exploration of counter examples of balanced sets" (2018). Honors Program Theses. 342.
Available for download on Monday, June 29, 2020