𝒮-adic characterization of minimal ternary dendric subshifts

02/19/2021

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by   France Gheeraert, et al.

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Dendric subshifts are defined by combinatorial restrictions of the extensions of the words in its language. This family generalizes well-known families of subshifts such as Sturmian subshifts, Arnoux-Rauzy subshifts and codings of interval exchange transformations. It is known that any minimal dendric subshifts 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 ot this family. We obtain such a characterization in the ternary case, involving a directed graph with 9 vertices.