Uniqueness in discrete tomography of Delone sets with long-range order.
Discrete and Computational Geometry, 42(4) pp. 740–758.
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.
||2009 Springer Science+Business Media, LLC
|Project Funding Details:
|Funded Project Name||Project ID||Funding Body|
|Combinatorics of Sequences and Tilings and its Applications||EP/D058465/1||EPSRC (Engineering and Physical Sciences Research Council)|
||discrete tomography; discrete parallel X-ray; U-polygon; algebraic Delone set; p-adic valuation; cyclotomic model set
||Mathematics, Computing and Technology > Mathematics and Statistics
||21 Sep 2010 13:11
||24 Mar 2014 13:53
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