A characterization of flip-accessibility for rhombus tilings of the whole plane

Authors:
Olivier Bodini;Thomas Fernique;Éric Rémila
Affiliations:
LIP6, CNRS, University of Paris 6, 4 place Jussieu 75005 Paris, France;LIRMM, CNRS, University of Montpellier 2, 161 rue Ada 34392 Montpellier Cedex 5, France;LIP, CNRS, INRIA, ENS Lyon, University of Lyon 1, 46 allée d'Italie 69364 Lyon Cedex 7, France
Venue:
Information and Computation
Year:
2008

Citing 3
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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.