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Document type:
Zeitschriftenaufsatz 
Author(s):
Alpers, A. and D.G. Larman 
Title:
The Smallest Sets of Points not Determined by Their X-rays 
Abstract:
Let F be an n-point set in Kd with K∈{R,Z} and d≥2. A (discrete) X-ray of F in direction s gives the number of points of F on each line parallel to s. We define ψKd(m) as the minimum number n for which there exist m directions s1,...,sm (pairwise linearly independent and spanning Rd) such that two n-point sets in Kd exist that have the same X-rays in these directions. The bound ψZd(m)≤2m−1 has been observed many times in the literature. In this note we show ψKd(m)=O(md+1+ε) for ε>0. For the case...    »
 
Journal title:
Bulletin of the London Mathematical Society 
Year:
2015 
Journal issue:
47 
Pages contribution:
171-176 
Reviewed:
ja 
Language:
en 
Publisher:
Wiley 
Status:
Postprint / reviewed 
TUM Institution:
Lehrstuhl für Angewandte Geometrie und Diskrete Mathematik