## Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

### Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)

### DMTCS Conference Volume AA (2001), pp. 287-300

author: | Gilles Radenne |
---|---|

title: | Tilings of a Domain on a Hexagon Mesh with Balanced 3-Tiles |

keywords: | Hexagon, Tiling, Balancing, Matching |

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]. |

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reference: | Gilles Radenne (2001), Tilings
of a Domain on a Hexagon Mesh with Balanced 3-Tiles, in
Discrete Models: Combinatorics, Computation, and
Geometry, DM-CCG 2001, Robert Cori and Jacques Mazoyer
and Michel Morvan and Rémy Mosseri (eds.),
Discrete Mathematics and Theoretical Computer Science
Proceedings AA, pp. 287-300 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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