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.

Authors and Affiliations

1. Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, USA

   Richard J. Gardner

2. Istituto per le Applicazioni del Calcolo, Sezione di Firenze, Via Madonna del Piano - CNR Edificio F, 50019 Sesto Fiorentino (FI), Italy

   Paolo Gronchi

3. School of Mathematics, Peking University, Beijing 100871, People’s Republic of China

   Chuanming Zong

Corresponding authors

Correspondence to Richard J. Gardner, Paolo Gronchi or Chuanming Zong.

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