A Characterization of Flip-Accessibility for Rhombus Tilings of the Whole Plane

Olivier Bodini 1 Thomas Fernique 2 Éric Rémila 3
2 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : It is known that any two rhombus tilings of a polygon are flip-accessible, \emph{i.e.} linked by a finite sequence of local transformations called flips. This paper considers flip-accessibility for rhombus tilings of the \emph{whole plane}, asking whether any two of them are linked by a \emph{possibly infinite} sequence of flips. The answer turning out to depend on tilings, a \emph{characterization} of flip-accessibility is provided. This yields, for example, that any tiling by Penrose tiles is flip-accessible from a Penrose tiling.
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Communication dans un congrès
LATA 2007 - 1st International Conference on Language and Automata Theory and Applications, Mar 2007, Tarragona, Spain. pp.139-150, 2007
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00149368
Contributeur : Thomas Fernique <>
Soumis le : vendredi 25 mai 2007 - 13:55:41
Dernière modification le : jeudi 22 novembre 2018 - 14:45:33
Document(s) archivé(s) le : jeudi 8 avril 2010 - 17:53:49

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Olivier Bodini, Thomas Fernique, Éric Rémila. A Characterization of Flip-Accessibility for Rhombus Tilings of the Whole Plane. LATA 2007 - 1st International Conference on Language and Automata Theory and Applications, Mar 2007, Tarragona, Spain. pp.139-150, 2007. 〈lirmm-00149368〉

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