128 citations
- Hebrew University of JerusalemIL2 papers
- Max Planck Institute for MathematicsDE2 papers
- Max Planck Institute for Mathematics in the SciencesDE2 papers
- Technische Universität BraunschweigDE2 papers
- Klinikum MagdeburgDE1 paper
- Max Planck Institute for Chemical Physics of SolidsDE1 paper
- Max Planck SocietyDE1 paper
- Osnabrück UniversityDE1 paper
- Otto-von-Guericke-Universität MagdeburgDE1 paper
- Shanghai Jiao Tong UniversityCN1 paper
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5 papers · 1 filter
Representing simple d-dimensional polytopes by d polynomials
Gennadiy Averkov, Martin Henk
A polynomial representation of a convex d-polytope P is a finite set \{p_1(x),...,p_n(x)\} of polynomials over E^d such that P=\setcond{x \in \E^d}{p_1(x) \ge 0 {for every} 1 \le i…
A Blichfeldt-type inequality for the surface area
Martin Henk, Joerg M. Wills
In 1921 Blichfeldt gave an upper bound on the number of integral points contained in a convex body in terms of the volume of the body. More precisely, he showed that $#(K\cap\Z^n)\…
Retrieving convex bodies from restricted covariogram functions
Gennadiy Averkov, Gabriele Bianchi
The covariogram g_K(x) of a convex body K \subseteq E^d is the function which associates to each x \in E^d the volume of the intersection of K with K+x. Matheron asked whether g_K…
Computational Approaches to Lattice Packing and Covering Problems
Achill Schuermann, Frank Vallentin
We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algor…
Polynomial inequalities representing polyhedra
Hartwig Bosse, Martin Groetschel, Martin Henk
Our main result is that every n-dimensional polytope can be described by at most (2n-1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For…