The fraction of an $S_n$-orbit on a hyperplane

Abstract

Huang, McKinnon, and Satriano conjectured that if $v\in {\mathbb{R}}^n$ has distinct coordinates and $n\ge 3$, then a hyperplane through the origin other than ${\sum }_i{x}_i=0$ contains at most $2\lfloor n/2\rfloor (n-2)!$ of the vectors obtained by permuting the coordinates of $v$. We prove this conjecture.

11 pages

References in corpus (1)

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