9 citations · 26 across the 10 of their papers we have counts for
11 papers
On the covering radius of lattice zonotopes and its relation to view-obstructions and the lonely runner conjecture
Matthias Henze, Romanos-Diogenes Malikiosis
The goal of this paper is twofold; first, show the equivalence between certain problems in geometry, such as view-obstruction and billiard ball motions, with the estimation of cove…
Tight bounds on discrete quantitative Helly numbers
Gennadiy Averkov, Bernardo González Merino, Matthias Henze +2
Given a subset S of R^n, let c(S,k) be the smallest number t such that whenever finitely many convex sets have exactly k common points in S, there exist at most t of these sets tha…
A generalization of the discrete version of Minkowski's fundamental theorem
Bernardo González Merino, Matthias Henze
One of the most fruitful results from Minkowski's geometric viewpoint on number theory is his so called 1st Fundamental Theorem. It provides an optimal upper bound for the volume o…
Partial-Matching and Hausdorff RMS Distance Under Translation: Combinatorics and Algorithms
Rinat Ben-Avraham, Matthias Henze, Rafel Jaume +4
We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-match…
On extensions of Minkowski's theorem on successive minima
Martin Henk, Matthias Henze, María A. Hernández Cifre
Minkowski's 2nd theorem in the Geometry of Numbers provides optimal upper and lower bounds for the volume of a -symmetric convex body in terms of its successive minima. In this…
Bottleneck Partial-Matching Voronoi Diagrams and Applications
Matthias Henze, Rafel Jaume
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We re…
A remark on perimeter-diameter and perimeter-circumradius inequalities under lattice constraints
Bernardo González Merino, Matthias Henze
In this note, we study several inequalities involving geometric functionals for lattice point-free planar convex sets. We focus on the previously not addressed cases perimeter--dia…
On counterexamples to a conjecture of Wills and Ehrhart polynomials whose roots have equal real parts
Matthias Henze
As a discrete analog to Minkowski's theorem on convex bodies, Wills conjectured that the Ehrhart coefficients of a centrally symmetric lattice polytope with exactly one interior la…
A Blichfeldt-type inequality for centrally symmetric convex bodies
Matthias Henze
In this note, we derive an asymptotically sharp upper bound on the number of lattice points in terms of the volume of centrally symmetric convex bodies. Our main tool is a generali…
Face numbers of centrally symmetric polytopes from split graphs
Ragnar Freij, Matthias Henze, Moritz W. Schmitt +1
We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's 3^d-conjecture for such polytopes (they all have at least 3…
Notes on lattice points of zonotopes and lattice-face polytopes
Christian Bey, Martin Henk, Matthias Henze +1
Minkowski's second theorem on successive minima gives an upper bound on the volume of a convex body in terms of its successive minima. We study the problem to generalize Minkowski'…