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arXiv · 1707.00931

Hook formulas for skew shapes III. Multivariate and product formulas

Alejandro H. Morales·Igor Pak·Greta Panova
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Abstract

We give new product formulas for the number of standard Young tableaux of certain skew shapes and for the principal evaluation of the certain Schubert polynomials. These are proved by utilizing symmetries for evaluations of factorial Schur functions, extensively studied in the first two papers in the series "Hook formulas for skew shapes" [arxiv:1512.08348, arxiv:1610.04744]. We also apply our technology to obtain determinantal and product formulas for the partition function of certain weighted lozenge tilings, and give various probabilistic and asymptotic applications.

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Alejandro H. Morales, Igor Pak, Greta Panova. 2020-06-02. Hook formulas for skew shapes III. Multivariate and product formulas. https://arxiv.org/abs/1707.00931

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