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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, that is, linked by a finite sequence of local transformations called flips. This paper considers flip-accessibility for rhombus tilings of the whole plane, asking whether any two of them are linked by a possibly infinite sequence of flips. The answer turning out to depend on tilings, a 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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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00379207
Contributor : Thomas Fernique <>
Submitted on : Tuesday, April 28, 2009 - 8:45:43 AM
Last modification on : Thursday, November 21, 2019 - 2:32:47 AM

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Olivier Bodini, Thomas Fernique, Éric Rémila. A Characterization of Flip-accessibility for Rhombus Tilings of the Whole Plane. Information and Computation, Elsevier, 2008, Special Issue: 1st International Conference on Language and Automata Theory and Applications (LATA 2007), 206 (9-10), pp.1065-1073. ⟨10.1016/j.ic.2008.03.008⟩. ⟨lirmm-00379207⟩

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