Bounding the Average Kissing Number, Including New Bounds for Three-Dimensional Binary Sphere Packings

Author

• Mark William Bockhaus, The University of Texas Rio Grande Valley

Date of Award

5-1-2026

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Alexey Glazyrin

Second Advisor

Luigi Ferraro

Third Advisor

Alexey Garber

Abstract

The average kissing number is defined as the supremum over all sphere packings of the value: two times the number of tangencies divided by the number balls in the packing. In this paper, we present a survey of the literature about bounding the average kissing number, beginning with the first non-trivial results, through the most up-to-date bounds. We then turn our focus to binary sphere packings: those which contain spheres of two different radii. We improve upon known bounds for the average kissing number for binary sphere packings in three-dimensions and find exact bounds for many packings.

Comments

Copyright 2026 Mark William Bockhaus. All Rights Reserved. https://proquest.com/docview/3371183904

Recommended Citation

Bockhaus, M. W. (2026). Bounding the Average Kissing Number, Including New Bounds for Three-Dimensional Binary Sphere Packings [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1889