Researcher ORCID Identifier

Graduation Year


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science



Reader 1

Mohamed Omar

Reader 2

Arthur T. Benjamin

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Terms of Use for work posted in Scholarship@Claremont.

Rights Information

2021 Thomas C Martinez


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.