Improved Bound for Tomaszewski's Problem
Improved Bound for Tomaszewski's Problem
In 1986, Tomaszewski made the following conjecture. Given $n$ real numbers $a_{1},\ldots,a_{n}$ with $\sum_{i=1}^{n}a_{i}^{2}=1$, then of the $2^{n}$ signed sums $\pm a_{1} \pm \cdots \pm a_{n}$, at least half have absolute value at most 1. Hendriks and van Zuijlen [An Improvement of the Boppana-Holzman Bound for Rademacher Random Variables}, arXiv:2003.02588, …