The Narayana Morphism and Related Words

Abstract: The Narayana morphism $\nu$ maps $0 \rightarrow 01$, $1 \rightarrow 2$, $2 \rightarrow 0$ and has a fixed point $$\mathbf{n} = n_0 n_1 n_2 \cdots = {\tt 0120010120120}\cdots$$. In this paper we study the properties of this word and related words using automata theory.