Maximum Density Space Packing with Parallel Strings of Spheres.
Mean Projections and Finite Packings of Convex Bodies.
Mehrfache gitterförmige Kreis- und Kugelanordnungen.
Metric Entropy of Homogeneous Spaces
For a precompact subset K of a metric space and ε > 0, the covering number N(K,ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In this paper we give asymptotically correct estimates for covering numbers for a large class of homogeneous...
Minimum Area of Circumscribed Polygons.
...-Morphic Sets of Prototiles.
Multiple Lattice Packings and Coverings of Spheres.
Multiple tilings by cubes with no shared faces.
Multiple Tilings of n-Dimensional Space by Unit Cubes.
New conjectural lower bounds on the optimal density of sphere packings.
New Upper Bounds for Some Spherical Codes
The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases...
New upper bounds on sphere packings. II.
Non-integer lattice tilings by (k, n) truncated crosses.
Nontiles and nonfacets for the Euclidean space, spherical complexes and convex polytopes.
Note on Packing of 19 Equal Circles on a Sphere.
Note to a paper of Bambah, Rogers and Zassenhaus
Notions of denseness.
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.