Optimal densities of packings consisting of highly unequal objects
Abstract
Let $\Delta$ be the optimal packing density of $\mathbb R^n$ by unit balls. We show the optimal packing density using two sizes of balls approaches $\Delta + (1  \Delta) \Delta$ as the ratio of the radii tends to infinity. More generally, if $B$ is a body and $D$ is a finite set of bodies, then the optimal density $\Delta_{\{rB\} \cup D}$ of packings consisting of congruent copies of the bodies from $\{rB\} \cup D$ converges to $\Delta_D + (1  \Delta_D) \Delta_{\{B\}}$ as $r$ tends to zero.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.01094
 Bibcode:
 2016arXiv160301094D
 Keywords:

 Mathematics  Metric Geometry;
 52C17