论文标题
改善了tomaszewski的问题
Improved Bound for Tomaszewski's Problem
论文作者
论文摘要
1986年，Tomaszewski做出了以下猜想。给定的$ n $实数$ a_ {1}，...，a_ {n} $带有$ \ sum_ {i = 1}^{n} a_ {i}^{2} = 1 $，然后在$ 2^{n} $中，然后$ 2^{n} $ sums $ sums $ \ pm a_ pm a_ {1} {1} \ pm pm ... Hendriks和Van Zuijlen（2020）和Boppana（2020）独立证明，这些款项中至少$ 0.4276 $的比例最多具有绝对的价值，最多为1美元。使用不同的技术，我们将其提高到$ 0.46 $。
In 1986, Tomaszewski made the following conjecture. Given $n$ real numbers $a_{1},...,a_{n}$ with $\sum_{i=1}^{n}a_{i}^{2}=1$, then of the $2^{n}$ signed sums $\pm a_{1} \pm ... \pm a_{n}$, at least half have absolute value at most $1$. Hendriks and Van Zuijlen (2020) and Boppana (2020) independently proved that a proportion of at least $0.4276$ of these sums has absolute value at most $1$. Using different techniques, we improve this bound to $0.46$.
