More characterizations of morphic words

Abstract

An interesting phenomenon in combinatorics on words is when every recurrent word satisfying some avoidance constraints has the same factor set as a morphic word. An early example is the Hall-Thue word, fixed point of the morphism $\text{0}\to \text{012}$, $\text{1}\to \text{02}$, $\text{2}\to \text{1}$, which is essentially the only ternary word avoiding squares and the words \texttt{010} and \texttt{212}. We provide some examples of this phenomenon from various contexts.