S-adic characterization of minimal ternary dendric shifts

2021/02/19 by France Gheeraert, Gheeraert, France, Marie Lejeune +3 · 2 citations
Mathematics · #37B10 #68R15 #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2102.10092

openalex publication_date 2021/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux-Rauzy shifts and codings of interval exchange transformations. It is known that any minimal dendric shift has a primitive S-adic representation where the morphisms in S are positive tame automorphisms of the free group generated by the alphabet. In this paper we investigate those S-adic representations, heading towards an S-adic characterization of this family. We obtain such a characterization in the ternary case, involving a directed graph with 2 vertices.

Cited by

• Extended branching Rauzy induction
• Automata on S-adic words

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