Upper Bounds for Non-Congruent Sphere Packings

Abstract

We prove upper bounds on the average kissing number $k(\mathcal{P})$ and contact number $C(\mathcal{P})$ of an arbitrary finite non-congruent sphere packing $\mathcal{P}$, and prove an upper bound on the packing density $\delta (\mathcal{P})$ of an arbitrary infinite non-congruent sphere packing $\mathcal{P}$.

6 pages

References in corpus (1)

• Upper bounds for packings of spheres of several radii

Cited by in corpus (1)

• On Arrangements of Six, Seven, and Eight Spheres: Maximal Bonding of Monatomic Ionic Compounds