Wednesday, Jan. 29 | 4-5 p.m. | Bridges 268

The Math Seminar continues on Wednesday January 29, when Professor Megan Jensen will speak about Young Tableaux and Hook-Length Formulas.

Captain Hook-Length Formula and His Skew Shaped Crew

Megan Jensen
Minnesota State University Moorhead

Abstract

Standard Young Tableaux (SYT) are fascinating combinatorial objects, that are simple to define but are have many deep properties that illuminate behavior of related combinatorial objects. For many years, an exact enumeration of the number of SYT of a particular shape remained elusive until a beautiful connection with hooks and hook-lengths were found. This enumeration was found by Frame, Robison, and Thrall in 1954. Recently, Naruse found a hook-length formula for the number of skew shaped standard Young tableaux, which was followed by a series of papers, where Morales, Pak, and Panova prove the Naruse hook-length formula.

In this talk we will explore the hook-length formula and explore connections between excited diagrams and Dyck paths.