Lozenge Tiling Function Ratios for Hexagons with Dents on Two Sides

2020/02/05 by Daniel J. Condon, Condon, Daniel · 2 citations
Materials Science · Mathematics · #05A-02 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2002.01988

openalex publication_date 2020/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

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

Related

• Lozenge tilings of hexagons with arbitrary dents
• Simple Relationships Between Lozenge Tiling Functions of Related Regions
• Tilings of hexagons with a removed triad of bowties
• Lozenge tilings of hexagons with holes on three crossing lines
• Lozenge tilings of hexagons with central holes and dents