2017/07/31 by Alejandro H. Morales, Igor Pak, Greta Panova
Mathematics · #math.CO
published as Algebraic Combinatorics, Volume 2 (2019) no. 5, pp. 815-861 · 40 pages, 17 figures. This is the third paper in the series "Hook formulas for skew shapes"; v2 added reference to [KO1] (arxiv:1409.1317) where the formula in Corollary 1.1 had previously appeared; v3 Corollary 5.10 added, resembles published version
arxiv created 2020/06/02 · arxiv updated 2020/06/03
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.