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Tilings of a domain on a hexagon mesh with balanced 3-tiles. (English) Zbl 1052.68776

Discrete models: combinatorics, computation, and geometry. Proceedings of the 1st international conference (DM-CCG), Paris, France, July 2–5, 2001. Paris: Maison de l’Informatique et des Mathématiques Discrètes (MIMD). Discrete Math. Theor. Comput. Sci., Proc. AA, 287-300, electronic only (2001).
Summary: In this article, we study the question of tilings on a hexagon mesh with balanced 3-tiles. This problem has been studied by Conway and Lagarias, by studying the tiling groups, in fact a group containing the tiling-groups, and their Cayley graphs. We use two different approaches. The first one is based on matchings in bipartite graphs, which in this case are in correspondance with tilings of domains by lozenges, and thus can be efficiently studied, using Thurston’s algorithm. The second one is based on a color and balancing approach of Thurston’s algorithm.
For the entire collection see [Zbl 0985.00015].

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68W05 Nonnumerical algorithms
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