Finite Coverings by Translates of Centrally Symmetric Convex Domains.
Finite Sphere Packing and Sphere Covering.
Finite sphere packings and critical radii.
Fourier analysis, linear programming, and densities of distance avoiding sets in
We derive new upper bounds for the densities of measurable sets in which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new upper bounds for measurable sets which avoid the unit distance in dimensions . This gives new lower bounds for the measurable chromatic number in dimensions . We apply it to get a short proof of a variant of a recent result of Bukh which in turn generalizes theorems of Furstenberg,...
Generalized Vitali systems of uniform type
Generalized Whitney partitions
We prove that the upper Minkowski dimension of a compact set Λ is equal to the convergence exponent of any packing of the complement of Λ with polyhedra of size not smaller than a constant multiple of their distance from Λ.
Gitterzahlen und innere Volumina.
Highly Saturated Packings and Reduced Coverings.
Horoball packings for the Lambert-cube tilings in the hyperbolic 3-space.
How To Build a Barricade.
How to cage an egg.
Improved Bounds for the Disk-packing Constant
Inhomogeneous extreme forms
G.F. Voronoi (1868–1908) wrote two memoirs in which he describes two reduction theories for lattices, well-suited for sphere packing and covering problems. In his first memoir a characterization of locally most economic packings is given, but a corresponding result for coverings has been missing. In this paper we bridge the two classical memoirs.By looking at the covering problem from a different perspective, we discover the missing analogue. Instead of trying to find lattices giving economical...
Ionpackings in the space
John Horton Conway (1937–2020)
Angloamerický matematik John Horton Conway byl všestrannou a charismatickou postavou, která významně ovlivnila teorie čísel, grup, her, uzlů, dynamických systémů i rekreační matematiku. Proslul svéráznou povahou i nekonvenčním přístupem k řešení problémů. Tento článek shrnuje stručně jeho neobvyklou životní cestu a představuje čtyři vybrané oblasti z jeho bohaté tvorby: nadreálná čísla, teorii kombinatorických her, hru života a klasifikaci sporadických grup.
Konvexe Fundamentalpolyeder und einfache D-V-Zellen für 29 Raumgruppen, die Coxetersche Spiegelungsuntergruppen enthalten
Lattice packings with gap defects are not completely saturated.
Locally Countable Plump Tilings are Flat.
Lockere gitterförmige k-fache Kreis- und Kugelüberdeckungen
Low-Degree Minimum Spanning Trees.