Brendan Pawlowski: The fraction of an S_n-orbit on a hyperplane
Abstract
Huang, McKinnon, and Satriano conjectured that if a real
vector (v_1, ..., v_n) has distinct coordinates and n ≥ 3, then a
hyperplane through the origin other than x_1 + ... + x_n = 0 contains
at most 2(n−2)!floor(n/2) of the vectors obtained by permuting the
coordinates of v. I will discuss a proof of this conjecture.