论文标题
在$ b_ {h} [1] $ - $ sets，是订单$ 2H $的渐近基础
On $B_{h}[1]$-sets which are asymptotic bases of order $2h$
论文作者
论文摘要
令$ h，k \ ge 2 $为整数。如果每个大大的正整数都可以写为$ k $ en $ k $ en $ a $ a $ a $ a $，则$ a $ a $ a $ a的正整数称为订单$ k $的渐近基础。一组正整数$ a $被认为是$ b_ {h} [g] $ - 如果每个正整数都可以写为$ a $的$ h $项的总和，则最多可以以$ g $ g $不同的方式。在本文中，我们证明了$ b_ {h} [1] $集的存在，这些$ sets是订单$ 2H $的渐近基础，并使用概率方法。
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.
