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

Sebastien Desreux·Martin Matamala·Ivan Rapaport·Eric Remila
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Abstract

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).

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Sebastien Desreux, Martin Matamala, Ivan Rapaport, Eric Remila. 2003-02-27. Domino tilings and related models: space of configurations of domains with holes. https://arxiv.org/abs/math/0302344

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