Undergrad-Thesis

The classical hook-length formula from the 1950s, counting the number of standard young tableaux of straight shapes is one of the beautiful results in Enumerative Combinatorics. Unlike the straight shapes, there isn't an elegant product formula for skew shapes yet. Okounkov and Olshanski found a positive formula for enumerating the standard young tableaux of skew shapes in 1996. Only recently in 2014, Naruse introduced another formula to count the number of standard young tableaux of skew shapes as a positive sum over excited diagrams of products of hook-lengths. We study these formulas and hope to gain more insight into the graph representations and observed bijections with Young's Lattice.