有限生成子群作为形式语言及其共增长
Finitely generated subgroups of free groups as formal languages and their cogrowth
AI总结：
本文研究自由群有限生成子群的正则语言，通过Schreier图核构造最小自动机，刻画不可约情形并给出计算共增长级数与熵的有效方法。
摘要：
对于有限秩$m$的自由群$F_m$的有限生成子群$H$，我们研究表示$H$的约化词的语言$L_H$，这是一个正则语言。利用$H$的Schreier图的（扩展）核，我们构造了识别$L_H$的最小确定性有限自动机。然后我们刻画了使得$L_H$不可约的有限生成子群$H$，并对此类群显式构造了识别$L_H$的遍历自动机。这一构造为我们提供了计算$H$的共增长级数$L_H(z)$及$L_H$的熵的有效方法。几个例子说明了该方法，并与基于$H$的Nielsen生成系计算$L_H(z)$的方法进行了比较。
英文摘要：
For finitely generated subgroups $H$ of a free group $F_m$ of finite rank $m$, we study the language $L_H$ of reduced words that represent $H$ which is a regular language. Using the (extended) core of Schreier graph of $H$, we construct the minimal deterministic finite automaton that recognizes $L_H$. Then we characterize the f.g. subgroups $H$ for which $L_H$ is irreducible and for such groups explicitly construct ergodic automaton that recognizes $L_H$. This construction gives us an efficient way to compute the cogrowth series $L_H(z)$ of $H$ and entropy of $L_H$. Several examples illustrate the method and a comparison is made with the method of calculation of $L_H(z)$ based on the use of Nielsen system of generators of $H$.
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。
