Séminaire Lotharingien de Combinatoire, 84B.93 (2020), 12 pp.
Alejandro H. Morales and Daniel Zhu
On the Okounkov-Olshanski Formula for Standard Tableaux of Skew Shapes
Abstract.
The classical hook-length formula counts the number of standard tableaux of straight shapes, but there is no known product formula for skew shapes. Okounkov-Olshanski (1996) and Naruse (2014) found new positive formulas for the number of standard Young tableaux of a skew shape. We prove various properties of the Okounkov-Olshanski formula: a reformulation similar to the Naruse formula, determinantal formulas for the number of terms, and a q-analogue extending the formula to reverse plane partitions, which complements work by Chen and Stanley for semistandard tableaux.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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