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arXiv · 1402.2183

Discrete tomography: Magic numbers for $N$-fold symmetry

Christian Huck·Markus Moll·Johan Nilsson
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Abstract

We consider the problem of distinguishing convex subsets of $n$-cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. In this context, a `magic number' $m_{\varLambda}$ has the property that any two convex subsets of $\varLambda$ can be distinguished by their X-rays in any set of $m_{\varLambda}$ prescribed $\varLambda$-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 $N=\operatorname{lcm}(n,2)$.

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Christian Huck, Markus Moll, Johan Nilsson. 2014-02-10. Discrete tomography: Magic numbers for $N$-fold symmetry. https://doi.org/10.12693/aphyspola.126.486

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