The countability of a tiling family and the periodicity of a tiling (original) (raw)

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Abstract

If a given finite protoset, together with a given finite matching rule, gives rise to at most countably many different tilings of_d_-dimensional space, then at least one of them is periodic.

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References

1. K. Böröczky, Gömbkitöltések állandó görbületű terekben I, II,Mat. Lapok,25 (1974), 265–306,26(1975), 67–90.
   Google Scholar
2. L. Danzer, Three-dimensional analogs of the planar Penrose tilings and quasicrystals,Discrete Math.,76 (1989), 1–7.
   Article MathSciNet MATH Google Scholar
3. M. Senechal,Quasicrystals and Geometry, Cambridge University Press, Cambridge, 1994.
   MATH Google Scholar

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Authors and Affiliations

1. Steklov Institute, 117333, Moscow, Russia
   N. Dolbilin

Additional information

This research was supported in part by the SFB 343 “Diskrete Strukturen in der Mathematik” at Bielefeld University and the Russian Foundation for Fundamental Research.

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Dolbilin, N. The countability of a tiling family and the periodicity of a tiling.Discrete Comput Geom 13, 405–414 (1995). https://doi.org/10.1007/BF02574052

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• Received: 17 February 1994
• Revised: 30 September 1994
• Published: 01 June 1995
• Issue date: June 1995
• DOI: https://doi.org/10.1007/BF02574052

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