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Periodicity of one-dimensional tilings

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Error Control, Cryptology, and Speech Compression (ECCSP 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 829))

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Abstract

The tiling problem is closely connected with a number of problems of information theory. We show that the Wang-Moore conjecture is valid for the one dimensional case. Namely, any set of templates which permits a tiling of the set ℤ of integers also permits a periodic tiling. We also show that any tiling of ℤ by one template is necessarily periodic. The obtained results are also valid for tiling of the set IR of real numbers.

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Authors and Affiliations

  1. Institute for Problems of Information Transmission, Ermolovoy St. 19, GSP-4, 101447, Moscow, Russia

    V. Sidorenko

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  1. V. Sidorenko
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Andrew Chmora Stephen B. Wicker

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© 1994 Springer-Verlag Berlin Heidelberg

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Sidorenko, V. (1994). Periodicity of one-dimensional tilings. In: Chmora, A., Wicker, S.B. (eds) Error Control, Cryptology, and Speech Compression. ECCSP 1993. Lecture Notes in Computer Science, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58265-7_14

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  • DOI: https://doi.org/10.1007/3-540-58265-7_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58265-6

  • Online ISBN: 978-3-540-48588-9

  • eBook Packages: Springer Book Archive

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