Manickam-Miklós-Singhi猜想的一个改进界
An improved bound for the Manickam-Miklós-Singhi conjecture
摘要：
我们证明了对于$n>k(4e\log k)^k$，每一个具有$\sum_{i=0}^{n}x_i \geq 0$的$n$实数集$\{x_1,..., x_n\}$至少有$\binom{n-1}{k-1}$ $k$ -元素子集的非负和。这是对先前已知的$n>(k-1)(k^k+k^2)+k$的最佳界限的实质性改进，该界限由Manickam和Miklós \cite{MM}在1987年证明。
英文摘要：
We show that for $n>k(4e\log k)^k$ every set $\{x_1,..., x_n\}$ of $n$ real numbers with $\sum_{i=0}^{n}x_i \geq 0$ has at least $\binom{n-1}{k-1}$ $k$-element subsets of a non-negative sum. This is a substantial improvement on the best previously known bound of $n>(k-1)(k^k+k^2)+k$, proved by Manickam and Miklós \cite{MM} in 1987.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
