S-adic characterization of minimal dendric shifts: an example

Minimal dendric shift spaces generalize both Arnoux-Rauzy spaces and codings of regular interval exchanges. They are defined using bipartite graphs, called extension graphs, describing the letters that we can see to the left and to the right of a (finite) word in the shift space. Berthé et al. proved that the family of minimal dendric shifts is stable under derivation, which leads to the construction of particular S-adic representations. In this talk, I will explain how to use these representations to obtain an S-adic characterization of minimal dendric shifts over an alphabet of any size. This is a joint work with Julien Leroy.