Researcher ORCID Identifier
0000-0002-5153-0533
Graduation Year
2023
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Mohamed Omar
Reader 2
Francis Edward Su
Terms of Use & License Information
Rights Information
© 2023 Tomás Aguilar-Fraga
Abstract
In combinatorics, it is often desirable to show that a sequence is unimodal. One method of establishing this is by proving the stronger yet easier-to-prove condition of being log-concave, or even ultra-log-concave. In 2019, Petter Brändén and June Huh introduced the concept of Lorentzian polynomials, an exciting new tool which can help show that ultra-log-concavity holds in specific cases. My thesis investigates these Lorentzian polynomials, asking in which situations they are broadly useful. It covers topics such as matroid theory, discrete convexity, and Mason’s conjecture, a long-standing open problem in matroid theory. In addition, we discuss interesting applications to known combinatorial objects and possible future paths for discovery.
Recommended Citation
Aguilar-Fraga, Tomás, "An Inquiry into Lorentzian Polynomials" (2023). HMC Senior Theses. 274.
https://scholarship.claremont.edu/hmc_theses/274
