On contact numbers of totally separable unit sphere packings
Karoly Bezdek, Balazs Szalkai, and Istvan Szalkai
TL;DR
This paper investigates the maximum number of contacts in totally separable packings of n unit spheres in Euclidean space, providing estimates applicable across all dimensions and sizes.
Contribution
It offers new estimates for contact numbers in totally separable sphere packings, extending understanding beyond previous specific cases.
Findings
Provides bounds for contact numbers in all dimensions and sizes
Extends known results on kissing numbers to separable packings
Offers a general framework for estimating contacts in sphere packings
Abstract
Contact numbers are natural extensions of kissing numbers. In this paper we give estimates for the number of contacts in a totally separable packing of n unit balls in Euclidean d-space for all n>1 and d>1.
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Taxonomy
TopicsPoint processes and geometric inequalities · Quasicrystal Structures and Properties · Advanced Materials and Mechanics