France Gheeraert ; Julien Leroy - S-adic characterization of minimal dendric shifts

dmtcs:13130 - Discrete Mathematics & Theoretical Computer Science, February 14, 2025, vol. 27:2 - https://doi.org/10.46298/dmtcs.13130
S-adic characterization of minimal dendric shiftsArticle

Authors: France Gheeraert ; Julien Leroy

    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 give an S-adic characterization of this family by means of two finite graphs. As an application, we are able to decide whether a shift space generated by a uniformly recurrent morphic word is (eventually) dendric.


    Volume: vol. 27:2
    Section: Combinatorics
    Published on: February 14, 2025
    Accepted on: January 10, 2025
    Submitted on: February 27, 2024
    Keywords: Mathematics - Dynamical Systems,Computer Science - Discrete Mathematics,68R15, 37B10

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