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2013 | OriginalPaper | Chapter

4. Magic Numbers in the Discrete Tomography of Cyclotomic Model Sets

Author : Christian Huck

Published in: Aperiodic Crystals

Publisher: Springer Netherlands

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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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Title: Magic Numbers in the Discrete Tomography of Cyclotomic Model Sets
Author: Christian Huck
Publisher: Springer Netherlands
Book: Aperiodic Crystals
Print ISBN: 978-94-007-6430-9

Electronic ISBN: 978-94-007-6431-6

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-94-007-6431-6_4

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