Factor properties and their structures are important themes in combinatorics on words. Let $\mathbb{D}$ be the infinite one-sided sequence over the alphabet $\{a,b\}$ generated by the period-doubling substitution $\sigma(a)=ab$ and $\sigma(b)=aa$. In this paper, we determine the derived sequence $D_w$($\mathbb{D}$) for any factor ω $\prec$ $\mathbb{D}$, and study some factor spectra using the structures of derived sequences. We also prove the reflexivity property of derived sequences.
Yuke HUANG
,
Zhiying WEN
. DERIVED SEQUENCES AND THE FACTOR SPECTRUM OF THE PERIOD-DOUBLING SEQUENCE[J]. Acta mathematica scientia, Series B, 2021
, 41(6)
: 1921
-1937
.
DOI: 10.1007/s10473-021-0609-z
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