自由群中的正则集与计数
Regular sets and counting in free groups
摘要：
本文研究了有限秩自由群F中正则子集的渐近行为，比较了它们在无穷远处的大小，并发展了计算集合相对于F上分布的概率的技巧，这些分布自然来自F的Cayley图上的无返回随机游动.我们应用这些技巧来研究F的n-生成子群的陪集、双陪集和Schreier表示，并分析F中正则前缀闭子集的相对大小。
英文摘要：
In this paper we study asymptotic behavior of regular subsets in a free group F of finite rank, compare their sizes at infinity, and develop techniques to compute the probabilities of sets relative to distributions on F that come naturally from no-return random walks on the Cayley graph of F. We apply these techniques to study cosets, double cosets, and Schreier representatives of finitely generated subgroups of F and also to analyze relative sizes of regular prefixed-closed subsets in F.
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