2003/02/27 by Sébastien Desreux, Sebastien Desreux, Martı́n Matamala +9
Computer Science · Materials Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Quasicrystal Structures and Properties #math.CO
paper · pdf · doi:10.48550/arxiv.math/0302344
17 pages, 11 figures
arxiv created 2003/02/27 · openalex publication_date 2003/02/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not necessarily local) transformations called \em flips. This study allows us to formulate an exhaustive generation algorithm and a uniform random sampling algorithm. We finally extend these results to other types of tilings (calisson tilings, tilings with bicolored Wang tiles).