Hook formulas for skew shapes III. Multivariate and product formulas

Morales, Alejandro H.; Pak, Igor; Panova, Greta

Algebraic Combinatorics, Tome 2 (2019) no. 5, pp. 815-861.

We give new product formulas for the number of standard Young tableaux of certain skew shapes and for the principal evaluation of 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 [54, 52]. 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.

Mots-clés : skew standard tableaux, product formulas, hook length, lozenge tilings, Schubert polynomials

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