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