Abstract
We report recent progress in the problem of distinguishing convex subsets of cyclotomic model sets Λ by (discrete parallel) X-rays in prescribed Λ-directions. It turns out that for any of these model sets Λ there exists a ‘magic number’ m Λ such that any two convex subsets of Λ can be distinguished by their X-rays in any set of m Λ prescribed Λ-directions. In particular, for pentagonal, octagonal, decagonal and dodecagonal model sets, the least possible numbers are in that very order 11, 9, 11 and 13.
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Acknowledgements
This work was supported by the German Research Council (Deutsche Forschungsgemeinschaft), within the CRC 701.
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Huck, C. (2013). Magic Numbers in the Discrete Tomography of Cyclotomic Model Sets. In: Schmid, S., Withers, R., Lifshitz, R. (eds) Aperiodic Crystals. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6431-6_4
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DOI: https://doi.org/10.1007/978-94-007-6431-6_4
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