Discrete Tomography: Magic Numbers for N-Fold Symmetry

Abstract

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