On the notion of the combinatorial -parametric property for polyhedra.
On the Number of Convex Lattice Polytopes.
On the number of intersections of two polygons
We study the maximum possible number of intersections of the boundaries of a simple -gon with a simple -gon in the plane for . To determine the number is quite easy and known when or is even but still remains open for and both odd. We improve (for ) the easy upper bound to and obtain exact bounds for
On the packing densities of superballs and other bodies.
On the perimeter of the intersection of congruent disks.
On the Representation and Multiplication of Basic Alternating Cycle Matrices
On the rigidity of one-dimensional systems of contraction similitudes.
On the section of a lattice–covering of balls
On the set of distances between two sets over finite fields.
On the shortest curve which meets all the lines which meet a circle
On the spectrum of the Thue-Morse quasicrystal and the rarefaction phenomenon
The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated by means of the Bombieri-Taylor conjecture, for Bragg peaks, and of a new conjecture that we call Aubry-Godrèche-Luck conjecture, for the singular continuous component. The decomposition of the Fourier transform of the weighted Dirac comb is obtained in terms of tempered distributions. We show that the asymptotic arithmetics of the -rarefied sums of the Thue-Morse sequence (Dumont; Goldstein, Kelly and Speer; Grabner;...
On the structure of sets with many k-term arithmetic progressions
On the thinnest 2-fold double-lattice covering with a centrally symmetric convex domain. (Über die dünnste doppelgitterförmige 2-fache Überdeckung mit einem zentralsymmetrischen konvexen Bereich.)
On the Zone of a Surface in a Hyperplane Arrangement.
On tropical Kleene star matrices and alcoved polytopes
In this paper we give a short, elementary proof of a known result in tropical mathematics, by which the convexity of the column span of a zero-diagonal real matrix is characterized by being a Kleene star. We give applications to alcoved polytopes, using normal idempotent matrices (which form a subclass of Kleene stars). For a normal matrix we define a norm and show that this is the radius of a hyperplane section of its tropical span.
On Two Finite Covering Problems of Bambah, Rogers, Woods and Zassenhaus.
On-line algorithms for the -adic covering of the unit interval and for covering a cube by cubes.
On-line covering a box by cubes.
On-Line Covering a Cube by a Sequence of Cubes.
On-Line Covering the Unit Cube by Cubes.