Young tableaux are combinatorial objects related to the partitions of an integer and have various applications in representation theory. They are particularly useful in the study of the fibers arising from the Springer resolution. In recent work of Graham-Precup-Russell, an association has been made between a given row-strict tableau and three disjoint subsets of {1,2,...,n}. These subsets are then used in the study of extended Springer fibers, so we call them extended sets. In this project, we use combinatorial techniques to classify which of these extended sets correlate to a valid row-strict or standard tableau and give bounds on the number of extended sets for a fixed size. We are able to identify several global properties of these valid sets, and we further find an algorithm that produces a valid tableau given the extended sets in special cases.

Author Bio

Eric Nofziger is a mathematics and computer science major at Butler University. His research was completed as part of his University Honors thesis in 2020-2022 with the help of his thesis advisor, Dr. Amber Russell. He is on the Butler Club Tennis team, writes for the Butler Collegian, and is a part of Phi Eta Sigma Honor Society.