Sums, Projections, and Sections of Lattice Sets, and the Discrete Covariogram

Sums, Projections, and Sections of Lattice Sets, and the Discrete Covariogram

Basic properties of finite subsets of the integer lattice Z n are investigated from the point of view of geometric tomography. Results obtained concern the Minkowski addition of convex lattice sets and polyominoes, discrete X-rays and the discrete and continuous covariogram, the determination of sym...

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Bibliographic Details
Published in:Discrete & computational geometry Vol. 34; no. 3; pp. 391 - 409
Main Authors: Gardner, Richard J., Gronchi, Paolo, Zong, Chuanming
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01-09-2005
Subjects:
Combinatorics
Geometry
Lattice theory
Tomography
Online Access:Get full text
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Summary:Basic properties of finite subsets of the integer lattice Z n are investigated from the point of view of geometric tomography. Results obtained concern the Minkowski addition of convex lattice sets and polyominoes, discrete X-rays and the discrete and continuous covariogram, the determination of symmetric convex lattice sets from the cardinality of their projections on hyperplanes, and a discrete version of Meyer's inequality on sections of convex bodies by coordinate hyperplanes. [PUBLICATION ABSTRACT]
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-005-1169-z