O jistém pokrytí racionálních bodů v rovině nekonečnou jednoduchou lomenou čarou
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 Connected with a Theorem of Jarnik.
On a problem of A.D. Sands.
On a problem of Ryškov concerning lattice coverings
On conjectures of Minkowski and Woods for n=8
On Convex Bodies that Permit Packings of High Density.
On coverings with convex domains
On Gauss's proof of Seeber's Theorem.
On geodesics of phyllotaxis
Seeds of sunflowers are often modelled by leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance for the golden ratio. We associate to such a map a geodesic path of the modular curve and use it for local descriptions of the image of the phyllotactic map .
On Linear Sections of Lattice Packings.
On lower bounds of the density of Delone sets and holes in sequences of sphere packings.
On Norm Three Vectors in Integral Euclidean Lattices. I.
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 Multiplicity of Lattices.
On the Euclidean minimum of some real number fields
General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.
On the lattice packing--covering ratio of finite-dimensional normed spaces
On the limit distribution of Frobenius numbers
On the Maximum of the Minimum of a Sum.
On the packing densities of superballs and other bodies.