𝒮-adic characterization of minimal dendric shifts

06/01/2022

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by   France Gheeraert, et al.

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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.