Ratio of tiling generating functions of semi-hexagons and quartered hexagons with dents

Abstract

We consider the tiling generating functions of semi-hexagons and quartered hexagons with dents on their sides. In general, there are no simple product formulas for these generating functions. However, we show that the modification in the regions' width changes the tiling generating functions by only a simple multiplicative factor.

Version 4: fixed some more typos

References in corpus (6)

• Condensation of Determinants
• A shuffling theorem for lozenge tilings of doubly-dented hexagons
• A Shuffling Theorem for Centrally Symmetric Tilings
• A Shuffling Theorem for Reflectively Symmetric Tilings
• Tiling Enumeration of Hexagons with Off-central Holes
• Lozenge Tiling Function Ratios for Hexagons with Dents on Two Sides

Cited by in corpus (3)

• A certain ratio of generating functions of lozenge tilings, obtained with non--intersecting lattice paths
• The quotient of generating functions of lozenge tilings for certain regions derived from hexagons, obtained with non--intersecting lattice paths
• Problems in the Enumeration of Tilings