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Number of results
2014 | 126 | 2 | 486-489

Article title

Discrete Tomography: Magic Numbers for N-Fold Symmetry

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EN

Abstracts

EN
We consider the problem of distinguishing convex subsets of n-cyclotomic model sets Λ by (discrete parallel) X-rays in prescribed Λ-directions. In this context, a 'magic number' m_{Λ} has the property that any two convex subsets of Λ can be distinguished by their X-rays in any set of m_{Λ} prescribed Λ-directions. Recent calculations suggest that (with one exception in the case n=4) the least possible magic number for n-cyclotomic model sets might just be N+1, where N=lcm(n,2).

Keywords

EN

Contributors

author
  • Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
author
  • Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
author
  • Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

References

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  • [2] P. Schwander, C. Kisielowski, M. Seibt, F.H. Baumann, Y. Kim, A. Ourmazd, Phys. Rev. Lett. 71, 4150 (1993), doi: 10.1103/PhysRevLett.71.4150
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  • [4] Huck, C. in: Aperiodic Crystals, Eds.: S. Schmid, R.L. Withers, R. Lifshitz, Springer, Dordrecht 2013, p. 29, doi: 10.1007/978-94-007-6431-6
  • [5] R.J. Gardner, P. Gritzmann, Trans. Am. Math. Soc. 349, 2271 (1997), doi: 10.1090/S0002-9947-97-01741-8
  • [6] M. Baake, U. Grimm, Aperiodic Order. Vol. 1. A Mathematical Invitation, Cambridge University Press, Cambridge 2013
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  • [8] C. Huck, Acta Crystallogr. A 65, 240 (2009), doi: 10.1107/S0108767309004292
  • [9] Y. Ishibashi, H. Sugiura, K. Saitoh, N. Tanaka, Philos. Mag. 91, 2519 (2011), doi: 10.1080/14786435.2010.523717
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Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.bwnjournal-article-appv126n215kz
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