Gábor Fejes Tóth, Lázló Fejes Tóth, Włodzimierz Kuperberg
Published 2022-02-22Version 1
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 dispute between Newton and Gregory about the maximum number of neighbors a member can have in a packing of congruent balls. Other problems ask for the average number of neighbors or the maximum number of mutually neighboring members in a packing. The present work gives a survey of these problems.
Double-normal pairs in space
The maximum number of points in the cross-polytope that form a packing set of a scaled cross-polytope
On the volume of unions and intersections of congruent balls under uniform contractions
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