Tomaszewski's Problem on Randomly Signed Sums: Breaking the 3/8 Barrier

Ravi B. Boppana, Ron Holzman

Let $v_1$, $v_2$, ..., $v_n$ be real numbers whose squares add up to 1. Consider the $2^n$ signed sums of the form $S=\sum \pm v_i$. Holzman and Kleitman (1992) proved that at le…