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Thursday, January 28, 2021

**Abstract:** The classical hook length formula counts the number of standard tableaux of straight shapes. In 1996, Okounkov and Olshanski found a positive formula for the number of standard Young tableaux of a skew shape. We prove various properties of this formula, including three determinantal formulas for the number of nonzero terms, an equivalence between the Okounkov-Olshanski formula and another skew tableaux formula involving Knutson-Tao puzzles, and two q-analogues for reverse plane partitions, which complements work by Stanley and Chen for semistandard tableaux. We also give applications and several reformulations of the formula, including two in terms of the excited diagrams appearing in a more recent skew tableaux formula by Naruse. This is joint work with Daniel Zhu. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.