Title

Universal lower bounds for potential energy of spherical codes

Document Type

Presentation

Presentation Date

Fall 10-14-2014

Conference Name

Minimal Energy Point Sets, Lattices, and Designs

Conference Location

Vienna, Austria

Publisher

Erwin Schrodinger International Institute for Mathematical Physics

Peer Review

Invited

Abstract

Based upon the works of Delsarte-Goethals-Seidel, Levenshtein, Yudin, and Cohn-Kumar we derive universal lower bounds for the potential energy of spherical codes, that are optimal (in the framework of the standard linear programming approach) over a certain class of polynomial potentials whose degrees are upper bounded via a familiar formula for spherical designs. We classify when improvements are possible employing polynomials of higher degree. Our bounds are universal in the sense of Cohn and Kumar; i.e., they apply whenever the potential is given by an absolutely monotone function of the inner product between pairs of points.

Keywords

potential energy, spherical codes, universal configurations

Disciplines

Analysis | Discrete Mathematics and Combinatorics