Pseudo-self-affine tilings in ℝd

B. Solomyak

doi:10.1007/s10958-007-0452-3

Pseudo-self-affine tilings in ℝ^d

B. Solomyak

University of Washington

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 Voronoï 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. Bibliography: 18 titles.

Original language	English
Pages (from-to)	452-460
Number of pages	9
Journal	Journal of Mathematical Sciences (United States)
Volume	140
Issue number	3
DOIs	https://doi.org/10.1007/s10958-007-0452-3
State	Published - Jan 2007
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgments. I am grateful to Jeong-Yup Lee and Lorenzo Sadun for helpful discussions. Supported in part by NSF grant #DMS-0355187.

Funding

Acknowledgments. I am grateful to Jeong-Yup Lee and Lorenzo Sadun for helpful discussions. Supported in part by NSF grant #DMS-0355187.

Funders	Funder number
National Science Foundation	-0355187

Access to Document

10.1007/s10958-007-0452-3

Cite this

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abstract = "It is proved that every pseudo-self-affine tiling in ℝd is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Vorono{\"i} 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. Bibliography: 18 titles.",

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