On a Uniqueness Problem in Discrete Tomography

Let A be a subset of the integer lattice Zn contained inside a sphere S in Rn. Suppose that for each u ∈ S we know the number of points of A visible from u. Does this information determine the set A uniquely? In this note we answer this question affirmatively, provided the center of the sphere is no...

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Bibliographic Details
Published in:The American mathematical monthly 2024-05, Vol.131 (5), p.440-444
Main Authors: Sun, Golden, Yaskin, Vladyslav
Format: Article
Language:English
Subjects:
Discrete element method
Integer programming
Mathematical functions
Mathematical problems
Tomography
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Summary:Let A be a subset of the integer lattice Zn contained inside a sphere S in Rn. Suppose that for each u ∈ S we know the number of points of A visible from u. Does this information determine the set A uniquely? In this note we answer this question affirmatively, provided the center of the sphere is not a rational point.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2024.2311446