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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, \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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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00149368
Contributor : Thomas Fernique <>
Submitted on : Friday, May 25, 2007 - 1:55:41 PM
Last modification on : Thursday, November 21, 2019 - 1:47:05 AM
Long-term archiving on: : Thursday, April 8, 2010 - 5:53:49 PM

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  • HAL Id : lirmm-00149368, version 1

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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. ⟨lirmm-00149368⟩

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