On the subword complexity of the fixed point of $a \rightarrow aab$, $b \rightarrow b$, and generalizations

Abstract

We find an explicit closed form for the subword complexity of the infinite fixed point of the morphism sending $a \rightarrow aab$ and $b \rightarrow b$. This morphism is then generalized in three different ways, and we find similar explicit expressions for the subword complexity of the generalizations.