关于$2h$阶渐近基的$B_{h}[1]$ -集
On $B_{h}[1]$-sets which are asymptotic bases of order $2h$
摘要：
令$h,k \ge 2$为整数。一个正整数集合$A$称为$k$阶渐近基，如果每一个足够大的正整数都可以表示为来自$A$的$k$项之和.一个正整数集合$A$称为$B_{h}[g]$ -集合，如果每个正整数都可以写成来自$A$至多$g$不同方式的$h$项之和。本文用概率方法证明了$2h$阶渐近基$B_{h}[1]$集的存在性。
英文摘要：
Let $h,k \ge 2$ be integers. A set $A$ of positive integers is called asymptotic basis of order $k$ if every large enough positive integer can be written as the sum of $k$ terms from $A$. A set of positive integers $A$ is said to be a $B_{h}[g]$-set if every positive integer can be written as the sum of $h$ terms from $A$ at most $g$ different ways. In this paper we prove the existence of $B_{h}[1]$ sets which are asymptotic bases of order $2h$ by using probabilistic methods.
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。
