Universal lower bounds for potential energy of spherical codes
Minimal Energy Point Sets, Lattices, and Designs
Erwin Schrodinger International Institute for Mathematical Physics
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.
potential energy, spherical codes, universal configurations
Analysis | Discrete Mathematics and Combinatorics
Peter Boyvalenkov, Peter D. Dragnev, Douglas P. Hardin, Edward B. Saff, and Maya Stoyanova (2014).
Universal lower bounds for potential energy of spherical codes. Erwin Schrodinger International Institute for Mathematical Physics.Presented at Minimal Energy Point Sets, Lattices, and Designs, Vienna, Austria.