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 $0\to 012$, $1\to 02$, $2\to 1$, which is essentially the only ternary word avoiding squares and the factors 010 and 212. We provide some examples of this phenomenon from various contexts.