Title

Packings in Real Projective Spaces

Document Type

Article

Publication Date

1-2018

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.

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.

DOI

10.1137/17M1137528

Source Publication

SIAM Journal on Applied Algebra and Geometry

Share

COinS