Abstract
Domino tilings of finite domains of the plane are used to model dimer systems in statistical physics. In this paper, we study dimer tilings, which generalize domino tilings and are indeed equivalent to perfect matchings of planar graphs. We use height functions, a notion previously introduced by Thurston in [10] for domino tilings, to prove that a dimer tiling of a given domain can be computed using any Single-Source-Shortest-Paths algorithm on a planar graph. We also endow the set of dimers tilings of a given domain with a structure of distributive lattice and show that it can be effectively visited by a simple algorithmical operation called flip.
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© 2006 Springer-Verlag Berlin Heidelberg
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Bodini, O., Fernique, T. (2006). Planar Dimer Tilings. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_13
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DOI: https://doi.org/10.1007/11753728_13
Publisher Name: Springer, Berlin, Heidelberg
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