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Lattice points. (English) Zbl 0798.52014

Gruber, P. M. (ed.) et al., Handbook of convex geometry. Volume B. Amsterdam: North-Holland. 765-797 (1993).
This article surveys various lattice point problems connected with convexity. Most of them concern convex lattice polytopes and the lattice point enumerator. Here are the main subjects discussed in the paper: Minkowski’s functional theorem and theorem on successive minima, bounds for lattice point enumerator in terms of intrinsic volumes, lattice polyhedra in combinatorial optimization, computational complexity of lattice point problems. Moreover, the authors provide a survey of equalities and inequalities concerning the diameter, the circumradius, the inradius and the minimum width of lattice-point-free convex bodies.
For the entire collection see [Zbl 0777.52002].

MSC:

52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
52C05 Lattices and convex bodies in \(2\) dimensions (aspects of discrete geometry)
68R99 Discrete mathematics in relation to computer science
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