Domino tilings and related models: space of configurations of domains with holes

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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).
17 pages, 11 figures

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Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/66648

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0302344
 http://arxiv.org/abs/math/0302344

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arXiv