S. Borodachov

collaborators

3 papers

math.CO2025

Universal polar dual pairs of spherical codes found in $E_{8}$ and $Λ_{24}$

S. V. Borodachov, P. G. Boyvalenkov, P. D. Dragnev +3

We identify universal polar dual pairs of spherical codes $C$ and $D$ such that for a large class of potential functions $h$ the minima of the discrete $h$ -potential of $C$ on the…

math.MG2024

Bounds on energy and potentials of discrete measures on the sphere

S. Borodachov, P. Boyvalenkov, P. Dragnev +3

We establish upper and lower universal bounds for potentials of weighted designs on the sphere $S^{n - 1}$ that depend only on quadrature nodes and weights derived from the…

math.MG2024

Bounds on Discrete Potentials of Spherical (k,k)-Designs

S. Borodachov, P. Boyvalenkov, P. Dragnev. D. Hardin. E. Saff +1

We derive universal lower and upper bounds for max-min and min-max problems (also known as polarization) for the potential of spherical $(k, k)$ -designs and provide certain examples…

Universal polar dual pairs of spherical codes found in E8​ and Λ24​

Bounds on energy and potentials of discrete measures on the sphere

Bounds on Discrete Potentials of Spherical (k,k)-Designs

Universal polar dual pairs of spherical codes found in $E_{8}$ and $Λ_{24}$