### Abstract

The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand, Wang tiles are used as a tool to generate textures and patterns in computer graphics. In these applications, a set of tiles is normally chosen so that it tiles the plane or its sub-regions easily in many different ways. With computer graphics applications in mind, we introduce a class of such tileset, which we call sequentially permissive tilesets, and consider tiling problems with constrained boundary. We apply our methodology to a special set of Wang tiles, called Brick Wang tiles, introduced by Derouet-Jourdan et al. in 2016 to model wall patterns. We generalise their result by providing a linear algorithm to decide and solve the tiling problem for arbitrary planar regions with holes.

Original language | English |
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Pages (from-to) | 749-761 |

Number of pages | 13 |

Journal | Japan Journal of Industrial and Applied Mathematics |

Volume | 36 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1 2019 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)
- Applied Mathematics

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## Cite this

*Japan Journal of Industrial and Applied Mathematics*,

*36*(3), 749-761. https://doi.org/10.1007/s13160-019-00369-z