Lattices of tilings : an extension to figures with holes

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. Afterwards, we give a geometrical interpretation of the order given by this lattice. We extend these results to other types of tilings (calisson tilings, tilings with bicolored Wang tiles).
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Eric Rémila. Lattices of tilings : an extension to figures with holes. [Research Report] LIP RR-2001-48, Laboratoire de l'informatique du parallélisme. 2001, 2+15p. ⟨hal-02101896⟩

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