8 papers
Successive Minima and Best Simultaneous Diophantine Approximations
Iskander Aliev, Martin Henk
We study the problem of best approximations of a vector by rational vectors of a lattice whose common denominator is bounded. To this e…
Free planes in lattice sphere packings
Martin Henk
We show that for every lattice packing of -dimensional spheres there exists an -dimensional affine plane which does not meet any of the spheres in their interior,…
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…
Successive Minima and Lattice Points
Martin Henk
The main purpose of this note is to prove an upper bound on the number of lattice points of a centrally symmetric convex body in terms of the successive minima of the body. This bo…
On the Equations Defining Toric L.C.I. Singularities
Dimitrios I. Dais, Martin Henk
Based on Nakajima's Classification Theorem we describe the precise form of the binomial equations which determine toric locally complete intersection ("l.c.i'') singularities.
On the representation of polyhedra by polynomial inequalities
Martin Grötschel, Martin Henk
A beautiful result of Bröcker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every -dimensional polyhedron admit…