论文标题
具有最大数量有限不变或内部1-quasi不变套件的功能或超集
Functions with a maximal number of finite invariant or internally-1-quasi-invariant sets or supersets
论文作者
论文摘要
关于不变的套装的概念，称为$ k $ quasi-quasi-invariant set，在文献中已经出现了多次与小组动态有关的文献。在这种情况下获得的结果取决于动态是由组生成的事实。在我们的工作中，我们考虑了适用于套装$ i $的函数$ f $的动作的不变和1个quasi-quasi-invariant套装的概念。我们回答了以下类型的几个问题，其中$ k \ in \ {0,1 \} $：$ i $的每个有限子集的函数$ f $是什么？更限制的是，如果$ i = \ mathbb {n} $，$ i $的每个有限间隔都在内部 - $ k $ quasi-quasi-invariant的功能$ f $？最后，$ i $的每个有限子集都在内部内置有限的$ k $ quasi-quasi-quasi-invariant超集的功能$ f $？这与C. E. Praeger在团体行动的背景下进行的类似调查相似。
A relaxation of the notion of invariant set, known as $k$-quasi-invariant set, has appeared several times in the literature in relation to group dynamics. The results obtained in this context depend on the fact that the dynamic is generated by a group. In our work, we consider the notions of invariant and 1-internally-quasi-invariant sets as applied to an action of a function $f$ on a set $I$. We answer several questions of the following type, where $k \in \{0,1\}$: what are the functions $f$ for which every finite subset of $I$ is internally-$k$-quasi-invariant? More restrictively, if $I = \mathbb{N}$, what are the functions $f$ for which every finite interval of $I$ is internally-$k$-quasi-invariant? Last, what are the functions $f$ for which every finite subset of $I$ admits a finite internally-$k$-quasi-invariant superset? This parallels a similar investigation undertaken by C. E. Praeger in the context of group actions.
