On the lattice packing--covering ratio of finite-dimensional normed spaces
On the lattice rest of a convex body in , III
On the monotonicity of the volume of hyperbolic convex polyhedra.
On the Number of Convex Lattice Polytopes.
On the section of a lattice–covering of balls
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.
Points entiers dans les polytopes convexes
Points frontières de certains compacts convexes appartenant à un réseau, dans et
(p,q)-Punktsysteme in der Minkowskischen Ebene
Radiography of perfect lattices. (Radiographie des réseaux parfaits.)
Rank forms, closed zones and laminae
For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank quadratic forms which are extreme rays for the corresponding -type domain.
Sections of simplices.
Six lonely runners.
Spherical Complexes and Nonprojective Tone Varieties.
Splitting groups of prime order.
Substitutions, abstract number systems and the space filling property
In this paper we study multi-dimensional words generated by fixed points of substitutions by projecting the integer points on the corresponding broken halfline. We show for a large class of substitutions that the resulting word is the restriction of a linear function modulo and that it can be decided whether the resulting word is space filling or not. The proof uses lattices and the abstract number system associated with the substitution.
Successive Minima, Intrinsic Volumes, and Lattice Determinants.
Successive-Minima-Type Inequalities.
The critical determinant of the double paraboloid and Diophantine approximation in and .