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Measuring cones and other thick subsets in free groups

2016/03/09 by Elizaveta Frenkel, Frenkel, Elizaveta, Vladimir N. Remeslennikov +2
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #cs.FL #math.GR #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1603.03002

18 pages, 4 figures

arxiv created 2016/03/09 · openalex publication_date 2016/03/09 · arxiv updated 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept. We show how one can decompose an arbitrary regular subset of a finite rank free group into disjoint union of sets accepted by special automata or special monoids. These automata allow us to compute explicitly generating functions, λ-measures and Cesaro measure of thick monoids. Also we improve the asymptotic classification of regular subsets in free groups.

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