# 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.