3 citations · 5 across the 8 of their papers we have counts for
9 papers · 1 filter
Miscellaneous problems about packing and covering
Gábor Fejes Tóth, László Fejes Tóth, Włodzimierz Kuperberg
In this paper we discuss various special problems on packing and covering. Among others we survey the problems and results concerning finite arrangements, Minkowskian, saturated, c…
Neighbors
Gábor Fejes Tóth, Lázló Fejes Tóth, Włodzimierz Kuperberg
Two members of a packing are neighbors if they have a common boundary point. A multitude of problems arises in connection with neighbors in a packing. The oldest one concerns a dis…
Ball packings in hyperbolic space
Gábor Fejes Tóth, Lázló Fejes Tóth, Włodzimierz. Kuperberg
In hyperbolic space density cannot be defined by a limit as we define it in Euclidean space. We describe the local density bounds for sphere packings and we discuss the different a…
Four classic problems
Gábor Fejes Tóth, Włodzimierz. Kuperberg
In this work we survey four classic problems: Borsuk's partition problem, Tarski's plank problem, the Kneser--Poulsen problem on the monotonicity of the union of balls under a cont…
The set of packing and covering densities of convex disks
Włodzimierz Kuperberg
For every convex disk (a convex compact subset of the plane, with non-void interior), the packing density and covering density form an ordered pair of rea…
Dense packing of space with various convex solids
András Bezdek, Włodzimierz Kuperberg
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set in the plane or in space. The most commonl…
Lattice packings with gap defects are not completely saturated
Greg Kuperberg, Krystyna Kuperberg, Wlodzimierz Kuperberg
We show that a honeycomb circle packing in with a linear gap defect cannot be completely saturated, no matter how narrow the gap is. The result is motivated by an open probl…
An extremum property characterizing the n-dimensional regular cross-polytope
Wlodzimierz Kuperberg
In the spirit of the Genetics of the Regular Figures, by L. Fejes Tóth, we prove the following theorem: If points are selected in the -dimensional Euclidean ball so t…
Almost-tiling the plane by ellipses
Krystyna Kuperberg, Włodzimierz Kuperberg, Jiří Matoušek +1
For any delta > 1 we construct a periodic and locally finite packing of the plane with ellipses whose delta-enlargement covers the whole plane. This answers a question of Imre Bárá…