Sums, Projections, and Sections of Lattice Sets, and the Discrete Covariogram |
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| Authors: | Richard J Gardner Paolo Gronchi Chuanming Zong |
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| Institution: | (1) Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, USA;(2) Istituto per le Applicazioni del Calcolo, Sezione di Firenze, Via Madonna del Piano - CNR Edificio F, 50019 Sesto Fiorentino (FI), Italy;(3) School of Mathematics, Peking University, Beijing 100871, People’s Republic of China |
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| Abstract: | Basic properties of finite subsets of the integer lattice ℤn 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. |
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