论文标题
在整数中最大的无额子集问题上
On the largest sum-free subset problem in the integers
论文作者
论文摘要
令$ a \ subset \ mathbb {z} _ {> 0} $ size $ n $的$。据推测，对于任何$ c> 0 $和$ n $，$ a $都包含一个至少$ n/3 +c $的$ a $的$ n $。我们研究了这个问题，并找到了波尔加因结果的替代证明，即一个使$ c = 2/3 $。
Let $A \subset \mathbb{Z}_{>0}$ of size $n$. It is conjectured that for any $C >0$ and $n$ large enough that $A$ contains a sum-free subset of size at least $n/3 +C$. We study this problem and find an alternate proof of Bourgain's result that one make take $C=2/3$.
