Hook Formula For Skew Shapes

Abstract

The number of standard Young tableaux is given by the hook-length formula of Frame, Robinson, and Thrall. Recently, Naruse found a hook-length formula for the number of skew shaped standard Young tableaux. In a series of papers, Morales, Pak, and Panova prove the Naruse hook-length formula as well as q-analogues of Naruse's formula. In this paper, we will discuss their work, including connections between excited diagrams and Dyck paths.