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arXiv · 0906.2850

Regular sets and counting in free groups

Elizaveta Frenkel·Alexei G. Myasnikov·Vladimir N. Remeslennikov
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Abstract

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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Elizaveta Frenkel, Alexei G. Myasnikov, Vladimir N. Remeslennikov. 2009-06-16. Regular sets and counting in free groups. https://arxiv.org/abs/0906.2850

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