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

TL;DR

This paper derives explicit formulas for the subword complexity of the infinite fixed point of a specific morphism and its generalizations, advancing understanding of combinatorial properties of morphic sequences.

Contribution

It provides the first explicit closed-form expressions for the subword complexity of the fixed point of the morphism and its generalizations.

Findings

Explicit formulas for subword complexity of the fixed point.

Generalizations also have similar explicit complexity expressions.

Advances understanding of combinatorial properties of morphic sequences.

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.