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arXiv · 2102.10092

$\mathcal{S}$-adic characterization of minimal ternary dendric shifts

France Gheeraert·Marie Lejeune·Julien Leroy
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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 $\mathcal{S}$-adic representation where the morphisms in $\mathcal{S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper we investigate those $\mathcal{S}$-adic representations, heading towards an $\mathcal{S}$-adic characterization of this family. We obtain such a characterization in the ternary case, involving a directed graph with 2 vertices.

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France Gheeraert, Marie Lejeune, Julien Leroy. 2021-02-19. $\mathcal{S}$-adic characterization of minimal ternary dendric shifts. https://arxiv.org/abs/2102.10092

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