What fraction of an $S_n$-orbit can lie on a hyperplane?

Jiahui Huang, David McKinnon, Matthew Satriano

Consider the $S_n$-action on ${\mathbb{R}}^n$ given by permuting coordinates. This paper addresses the following problem: compute ${\max }_{v,H}|H\cap S_{n}v|$ as $H\subset {\mathbb{R}}^n$…