Lozenge Tiling Function Ratios for Hexagons with Dents on Two Sides (2002.01988v2)

Abstract: We give a formula for the number of lozenge tilings of a hexagon on the triangular lattice with unit triangles removed from arbitrary positions along two non-adjacent, non-opposite sides. Our formula implies that for certain families of such regions, the ratios of their numbers of tilings are given by simple product formulas.