On a Uniqueness Problem in Discrete Tomography

Abstract

Let A be a subset of the integer lattice ${\mathbb{Z}}^n$ contained inside a sphere S in ${\mathbb{R}}^n$. Suppose that for each $u\in S$ 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.

MSC:

• 52C07

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

ACKNOWLEDGMENT

The authors wish to thank the anonymous referees for many valuable suggestions.

Additional information

Notes on contributors

Golden Sun

GOLDEN (YAOXIN) SUN University of Alberta, Edmonton, AB T6G 2G1, Canada

[email protected]

Vladyslav Yaskin

VLADYSLAV YASKIN Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada

[email protected]