Date of Award

5-2022

Degree Type

Thesis

Degree Name

Honors Thesis

Department

Mathematics

First Advisor

Amber Russell

Abstract

Young tableaux are combinatorial objects related to the partitions of an integer that have various applications in representation theory. These tableaux are defined as a left-justified set of n boxes filled with the numbers 1 through n and organized in rows, with the length of each row corresponding to a summand in the partition. In recent work of Graham–Precup–Russell, an association has been made between a given row-strict tableau and three disjoint subsets I, J, and K, also called extended sets. In this project, we begin to classify which extended sets correlate to a valid row-strict or standard tableau. We are able to identify several global properties of these valid sets, and we further find an algorithm that produces a valid tableau given only the extended sets in special cases.

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