Uniqueness in discrete tomography of Delone sets with long-range order
Huck, Christian · Open Research Online (The Open University) · 2009
We address the problem of determining finite subsets of Delone sets Λ⊂ℝd with long-range order by X-rays in prescribed Λ-directions, i.e., directions parallel to nonzero interpoint vectors of Λ. Here, an X-ray in direction u of a finite set gives the number of points in the set on each line parallel to u. For our main result, we introduce the notion of algebraic Delone sets Λ⊂ℝ2 and derive a sufficient condition for the determination of the convex subsets of these sets by X-rays in four prescribed Λ-directions.