论文标题
最小补充的渐近行为
Asymptotic behaviour of minimal complements
论文作者
论文摘要
Nathanson在2011年引入了最小补充的概念，作为Nets公制概念的自然群体理论类似物。给定两个非空的子集$ w，w'$中的$ g $，如果$ w \ cdot w'= g $，set $ w'$是对$ w $的补充，如果没有适当的子集$ w'$是$ w $的补充，则它是最小的。反问题询问哪些集可能会随着最小的补充而发生。我们在反问题上显示了一些新的结果，并研究了反问题的研究自然会引起有关这些集合的渐近行为的问题，从而为其中一些情况提供了部分答案。
The notion of minimal complements was introduced by Nathanson in 2011 as a natural group-theoretic analogue of the metric concept of nets. Given two non-empty subsets $W,W'$ in a group $G$, the set $W'$ is said to be a complement to $W$ if $W\cdot W'=G$ and it is minimal if no proper subset of $W'$ is a complement to $W$. The inverse problem asks which sets may or not occur as minimal complements. We show some new results on the inverse problem and investigate how the study of the inverse problem naturally gives rise to questions about the asymptotic behaviour of these sets, providing partial answers to some of them.
