在给定的最小周期内，全班次中的配置数
The number of configurations in the full shift with a given least period
摘要：
对于任何组$G$和任何集合$A$，考虑$G$在全班$A^G$上的移位动作。如果$x$的稳定器正好是$H$，则配置$x \in A^G$具有\emph{least period} $H \leq G$。除其他事项外，这种配置的数量是有趣的，因为它提供了相应的$\text{Aut}(A^G)$轨道大小的上限。本文证明了，若$G$是双生成的，且$H$是有限指数的，则利用$G$中有限指数子群格的Möbius函数，可以计算出$A^G$中具有最小周期$H$的组态个数.此外，当$H$是正规子群时，我们对所有情形进行分类，使得具有最小周期$H$的$G$ -轨道的数目至多为$10$。
英文摘要：
For any group $G$ and any set $A$, consider the shift action of $G$ on the full shift $A^G$. A configuration $x \in A^G$ has \emph{least period} $H \leq G$ if the stabiliser of $x$ is precisely $H$. Among other things, the number of such configurations is interesting as it provides an upper bound for the size of the corresponding $\text{Aut}(A^G)$-orbit. In this paper we show that if $G$ is finitely generated and $H$ is of finite index, then the number of configurations in $A^G$ with least period $H$ may be computed using the Möbius function of the lattice of subgroups of finite index in $G$. Moreover, when $H$ is a normal subgroup, we classify all situations such that the number of $G$-orbits with least period $H$ is at most $10$.
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。
