Some properties of morphic images of (eventually) dendric words

TL;DR

This paper investigates how morphisms affect the complexity of eventually dendric words and characterizes morphisms that preserve dendricity, linking them to Arnoux-Rauzy morphisms.

Contribution

It analyzes the evolution of factor complexity under morphisms and identifies all morphisms that preserve dendricity as Arnoux-Rauzy generated.

Findings

Factor complexity changes under non-erasing morphisms are characterized.

Morphisms preserving dendricity are exactly the Arnoux-Rauzy morphisms.

Abstract

The class of (eventually) dendric words generalizes well-known families such as the Arnoux-Rauzy words or the codings of interval exchanges. There are still many open questions about the link between dendricity and morphisms. In this paper, we focus on two questions. The first one is the evolution of the factor complexity when applying a non-erasing morphism to an eventually dendric word. We next look at the morphisms that preserve dendricity for all dendric words and show that they are exactly those generated by the Arnoux-Rauzy morphisms.