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Uniqueness in discrete tomography of Delone sets with long-range order

Huck, Christian (2009). Uniqueness in discrete tomography of Delone sets with long-range order. Discrete and Computational Geometry, 42(4) pp. 740–758.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/s00454-009-9213-z
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Abstract

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.

Item Type: Journal Article
Copyright Holders: 2009 Springer Science+Business Media, LLC
ISSN: 1432-0444
Project Funding Details:
Funded Project NameProject IDFunding Body
Combinatorics of Sequences and Tilings and its ApplicationsEP/D058465/1EPSRC (Engineering and Physical Sciences Research Council)
Keywords: discrete tomography; discrete parallel X-ray; U-polygon; algebraic Delone set; p-adic valuation; cyclotomic model set
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 23206
Depositing User: Uwe Grimm
Date Deposited: 21 Sep 2010 13:11
Last Modified: 24 Mar 2014 13:53
URI: http://oro.open.ac.uk/id/eprint/23206
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