O ukladaní kociek a iných objektov
Uvedieme históriu a prehľad výsledkov o ukladaní kociek do kvádra s minimálnym objemom a pridáme aj hlavné myšlienky niektorých dôkazov. V závere sa veľmi stručne zmienime o iných ukladacích problémoch.
On a generalization of Craig lattices
In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range . We also construct some dense lattices of dimensions in the range . Finally we also obtain some new lattices of moderate dimensions such as , which are denser than the...
On a Problem About Covering Lines by Squares.
On a problem of Ryškov concerning lattice coverings
On billiard arcs
On Convex Bodies that Permit Packings of High Density.
On covering of bounded sets by sets with the twice less diameter
On coverings of plane convex sets by translates of strips.
On finite sphere-packings.
On Gauss's proof of Seeber's Theorem.
On homogeneous coverings of Euclidean spaces.
On -neighbour packings and one-sided Hadwiger configurations.
On kissing numbers in dimensions 32 to 128.
On lower bounds of the density of Delone sets and holes in sequences of sphere packings.
On minimum kissing numbers of finite translative packings of a convex body.
On mixed sphere packings.
On packing spheres into containers.
On rhombic dodecahedra.
On the construction of dense lattices with a given automorphisms group
We consider the problem of constructing dense lattices in with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions , we exhibit a finite set of lattices that come with an automorphisms group of size , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...
On the covering by small random intervals