Graph encoding of 2D-gon tilings.

Abstract : 2D-gons tilings with parallelograms are the main model used in physics to study quasicrystals, and they are also important in combinatorics for the study of aperiodic structures. In this paper, we study the graph induced by the adjacency relation between tiles. This relation can been used to encode simply and efficiently 2D-gon tilings for algorithmic manipulation. We show for example how it can be used to sample random 2D-gon tilings.
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Frédéric Chavanon, Matthieu Latapy, Michel Morvan, Laurent Vuillon. Graph encoding of 2D-gon tilings.. [Research Report] LIP RR-2003-43, Laboratoire de l'informatique du parallélisme. 2003, 2+17p. ⟨hal-02101899⟩

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