2024/10/16 by France Gheeraert, Gheeraert, France, Herman Goulet-Ouellet +5
Computer Science · #37B10 (Primary) 68R15 (Secondary) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2410.12534
openalex publication_date 2024/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of pseudorandom numbers (through the welldoc property), and of profinite invariants of shift spaces. Aiming at unifying disparate works, we introduce a notion of stability for subgroups generated by return words. Within this framework, we revisit several existing results and generalize some of them. We also study general aspects of stability, such as decidability or closure under certain operations.