Tilings of a Domain on a Hexagon Mesh with Balanced 3-TilesReport as inadecuate

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1 ENS Lyon - École normale supérieure - Lyon

Abstract : 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 in CL90, by studying the tiling groups, in fact a group containing the tiling-groups, and their Cayley graphs. We will 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 see Thu90. The second one is based on a color and balancing approach of Thurston-s algorithm, exposed in Fou96.

Keywords : Hexagon Tiling Balancing Matching

Author: Gilles Radenne -

Source: https://hal.archives-ouvertes.fr/


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