Kihyun Kim ’24 — This summer, I worked as a research assistant with my coworker Gabriel Cowley under Dr. Katie Ansaldi, studying combinatorial and number-theoretic approaches to the Rainbow Ramsey Theory. The Rainbow Ramsey Theory is a branch of combinatorics that focuses on the appearance of order in a specific size structure. The theorem conjectures that complete disorder is impossible so that we can find patterns within disarray.

Rainbow Ramsey Theory is one of many problems derived from Ramsey theory, finding interesting properties when the set of integers, 1 to n, is partitioned into c number of sets. C number of sets is called ‘colors,’ and the partitioning process is called coloring. To rephrase, in this theorem, every integer is assigned to a color, and we are checking whether there are any interesting properties in coloring. For example, this summer, our research group was dealing with solution sets of an equation, x-y = z^2. We studied patterns of assigning colors under a certain condition, such as avoiding assigning the same color twice to the numbers in a solution set.

Fortunately, our research group could discover multiple theorems and conjectures during the research. Furthermore, during the internship, I could get more than research experience or knowledge in Rainbow Ramsey Theory. Thanks to faculty members of the Department of Mathematics & Computer Science and the Department of Physics, including Dr. Westphal, Dr. Gates, Dr. McCartin-Lim, and Dr. Tompkins, mathematics and physics research interns got an opportunity to do a weekly presentation and learn how to give an academic presentation properly. From this experience, our research group is planning to participate in Indiana Undergraduate Math Research Conference on July 28th to present our research results.

In the last place, I want to thank the Wabash College Department of Mathematics & Computer Science and Dr. Ansaldi for allowing me to get a research experience. As a freshman who did not have any prior research experience, it was a great pleasure to have such an opportunity.