Codes and Expansions (CodEx) Seminar

Oleg Musin (University of Texas Rio Grande Valley):
Majorization and optimal spherical configurations

We consider the majorization (Karamata) inequality and minimums of the majorization (\(M\)-sets) for \(f\)-energy potentials of \(m\)-point configurations in a sphere. In particular, we discuss the optimality of regular simplexes, describe M-sets with a small number of points, define spherical \(f\)-design and study their properties. Then we consider relations between the notions of \(f\)-designs, \(M\)-sets, \(t\) -designs, and two-distance sets.