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THE ERDŐS-MOSER SUM-FREE SET PROBLEM
Canadian Journal of Mathematics ( IF 0.7 ) Pub Date : 2019-09-23 , DOI: 10.4153/s0008414x1900049x
Tom Sanders

Abstract We show that there is an absolute $c>0$ such that if $A$ is a finite set of integers, then there is a set $S\subset A$ of size at least $\log ^{1+c}|A|$ such that the restricted sumset $\{s+s^{\prime }:s,s^{\prime }\in S\text{ and }s\neq s^{\prime }\}$ is disjoint from $A$. (The logarithm here is to base $3$.)

中文翻译:

ERDŐS-MOSER 无和集问题

摘要 我们证明存在绝对 $c>0$ 使得如果 $A$ 是整数的有限集,则存在大小至少为 $\log ^{1+c} 的集合 $S\subset A$ |A|$ 使得受限和集 $\{s+s^{\prime }:s,s^{\prime }\in S\text{ and }s\neq s^{\prime }\}$ 是与 $A$ 脱节。(这里的对数是以 $3$ 为底的。)
更新日期:2019-09-23
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