Dendric words and strongly left proper morphisms

Given a language L, we associate to each word its extension graph in L. This graph describes the letters that we can see to the left and to the right of the word in L. If this graph is a tree, then we say that the word is dendric, and if all the elements of L are dendric, we say that L itself is dendric. This notion generalizes the well-studied Sturmian and Arnoux-Rauzy words, as well as the codings of regular interval exchanges.

Among all morphisms, strongly left proper morphisms have some recognizability property which makes the study of their images easier. In this talk, I will then present results related to images of dendric languages under strongly left proper morphisms, in order to obtain an S-adic characterization of dendric languages. This is a joint work with Julien Leroy.