Lozenge Tiling Function Ratios for Hexagons with Dents on Two Sides

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.

arXiv comment22 pages, 13 figures V2: Updated citations both in the references section and Section 1

Cited by in corpus (2)

• Ratio of tiling generating functions of semi-hexagons and quartered hexagons with dents
• Problems in the Enumeration of Tilings