Envelope Words and the Reflexivity of the Return Word Sequences in the Period-doubling Sequence

Yu-Ke Huang, Zhi-Ying Wen

We consider the infinite one-sided sequence over alphabet $\{a,b\}$ generated by the period-doubling substitution $\sigma (a)=ab$ and $\sigma (b)=aa$, denoted by $\mathbb{D}$. Let $r_p(\omega )$ be…