Yuchen Wei, Rutgers University

Abstract

What is the number of standard Young tableaux for a given partition? And why do we care about the number of standard Young tableaux? It turns out that we can quickly compute it by invoking the hook length formula which only involves the number of boxes in the partition and the hook lengths (isn't it nice?). To answer the second question, one reason is that the number of standard Young tableaux of a given partition is equal to the dimension of the irreducible representation (over the complex field) associated with the given partition! This reveals the true beauty of the hook length formula: combinatorics at one end and algebra on the other. But we will only focus on the combinatorics in the talk. I will sketch a short probabilistic proof then quickly move to an elegant bijective proof given by Igor Pak. Time permitting, we will also talk about the RSK as a corollary.

Presented via Zoom - Meeting ID: 984 4140 9199

https://rutgers.zoom.us/j/98441409199

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