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

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.