Researcher ORCID Identifier
https://orcid.org/0000-0002-5752-2470
Graduation Year
2021
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Mohamed Omar
Reader 2
Arthur T. Benjamin
Terms of Use & License Information
Rights Information
2021 Thomas C Martinez
Abstract
Suppose you wanted to bound the maximum size of a set in which every k-tuple of elements satisfied a specific condition. How would you go about this? Introduced in 2016 by Terence Tao, the slice rank polynomial method is a recently developed approach to solving problems in extremal combinatorics using linear algebraic tools. We provide the necessary background to understand this method, as well as some applications. Finally, we investigate a generalization of the slice rank, the partition rank introduced by Eric Naslund in 2020, along with various discussions on the intuition behind the slice rank polynomial method and other possible avenues for generalization.
Recommended Citation
Martinez, Thomas C., "The Slice Rank Polynomial Method" (2021). HMC Senior Theses. 245.
https://scholarship.claremont.edu/hmc_theses/245
