Magic Numbers in the Discrete Tomography of Cyclotomic Model Sets

  • Christian HuckEmail author


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.


High Resolution Transmission Electron Microscopy Convex Subset High Resolution Transmission Electron Microscopy Finite Subset Cross Ratio 
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This work was supported by the German Research Council (Deutsche Forschungsgemeinschaft), within the CRC 701.


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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