On a question by Corson about point-finite coverings

On Finite Lattice Coverings

We consider nite lattice coverings of strictly convex bodies K. For planar centrally symmetric K we characterize the nite arrangements Cn such that conv Cn Cn + K, where Cn is a subset of a covering lattice for K (which satisses some natural conditions). We prove that for a xed lattice the optimal arrangement (measured with the parametric density) is either a sausage, a socalled double sausage ...

Finite Groups with p-Sylow Coverings

On Point Coverings of Boxes in R

Families of boxes in R are considered. In the paper an upper bound on the size of a minimum transversal in terms of the space dimension and the independence number of the given family was improved. Given a family B of boxes with edges parallel to coordinate axes of R, let ν(B) denote the maximal number of pairwise disjoint members of B and τ(B) denote the minimal number of points in a set meeti...

Finite Coverings and Rational Points

The purpose of this talk is to put forward a conjecture. The background is given by the following Basic Question. Given a (smooth projective) curve C over a number field k, can we determine explicitly the set C(k) of rational points? One possible approach to this is to consider an unramified covering D π → C that is geometrically Galois. By standard theory, there are only finitely many twists D...

Finite Groupoids, Finite Coverings and Symmetries in Finite Structures

We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual sense, but with respect to a discounted distance measure that contracts arbitrarily long sequences of edges within the same sub-groupoid (coset) and only co...