Packings in Real Projective Spaces
Document Type
Article
Publication Date
7-24-2018
Abstract
This paper applies techniques from algebraic and differential geometry to determine how to best pack points in real projective spaces. We present a computer-assisted proof of the optimality of a particular 6-packing in $\mathbb{R}\mathbf{P}^3$, we introduce a linear-time constant-factor approximation algorithm for packing in the so-called Gerzon range, and we provide local optimality certificates for two infinite families of packings. Finally, we present perfected versions of various putatively optimal packings from Sloane's online database, along with a handful of infinite families they suggest, and we prove that these packings enjoy a certain weak notion of optimality. Abstract © SIAM.
Source Publication
SIAM Journal on Applied Algebra and Geometry
Recommended Citation
Fickus, M., Jasper, J., & Mixon, D. G. (2018). Packings in Real Projective Spaces. SIAM Journal on Applied Algebra and Geometry, 2(3), 377–409. https://doi.org/10.1137/17M1137528
Comments
Copyright statement: ©2018 Society for Industrial and Applied Mathematics
The "Link to Full Text" on this page loads the open access article hosted at the SIAM website.