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

Abstract

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

5 pages, 2 figures; new computer calculations based on the results of arXiv:1101.4149 and arXiv:1211.6318; presented at ICQ 12 (Cracow, Poland)

References in corpus (3)

• Magic numbers in the discrete tomography of cyclotomic model sets
• Discrete Tomography of Penrose Model Sets
• Discrete Tomography of Icosahedral Model Sets