SIAM Journal on Discrete Mathematics, Volume 35, Issue 3, Page 1578-1591, January 2021.
In the present paper, we consider the majorization theorem (also known as Karamata's inequality) and the respective minima of the majorization (the so-called $M$-sets) for $f$-energy potentials of $m$-point configurations on the unit sphere. In particular, we show the optimality of regular simplexes, describe some $M$-sets of small cardinality, and define and discuss spherical $f$-designs.

中文翻译：

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球体上的主化和最小能量

SIAM Journal on Discrete Mathematics，第 35 卷，第 3 期，第 1578-1591 页，2021
年1 月。在本文中，我们考虑了专业化定理（也称为 Karamata 不等式）和专业化的各自最小值（所谓的 $ M$-sets) 用于单位球体上 $m$-点配置的 $f$-能量势。特别是，我们展示了正则单纯形的最优性，描述了一些 $M$-小基数集，并定义和讨论了球形 $f$-设计。