Hidden symmetries of weighted lozenge tilings

Abstract

We study the weighted partition function for lozenge tilings, with weights given by multivariate rational functions originally defined by Morales, Pak and Panova (2019) in the context of the factorial Schur functions. We prove that this partition function is symmetric for large families of regions. We employ both combinatorial and algebraic proofs.

13 pages, 8 figures

References in corpus (4)

• Hook formulas for skew shapes I. $q$-analogues and bijections
• Shift-invariance for vertex models and polymers
• Hook formulas for skew shapes II. Combinatorial proofs and enumerative applications
• Determinants of weighted path matrices