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Pseudo-self-affine tilings in R^d

Boris Solomyak
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Abstract

It is proved that every pseudo-self-affine tiling in R^d is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronoi tessellations is a corollary. Previously, these results were obtained in the planar case, jointly with Priebe Frank. The new approach is based on the theory of graph-directed iterated function systems and substitution Delone sets developed by Lagarias and Wang.

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Boris Solomyak. 2005-10-02. Pseudo-self-affine tilings in R^d. https://arxiv.org/abs/math/0510014

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