DERIVED SEQUENCES AND THE FACTOR SPECTRUM OF THE PERIOD-DOUBLING SEQUENCE

doi:10.1007/s10473-021-0609-z

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 1921-1937.doi: 10.1007/s10473-021-0609-z

DERIVED SEQUENCES AND THE FACTOR SPECTRUM OF THE PERIOD-DOUBLING SEQUENCE

黄煜可¹, 文志英²

1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2021-03-29 修回日期:2021-07-21 出版日期:2021-12-25 发布日期:2021-12-27
通讯作者: Yuke HUANG,E-mail:hyk@bupt.edu.cn E-mail:hyk@bupt.edu.cn
作者简介:Zhiying WEN,E-mail:wenzy@tsinghua.edu.cn
基金资助:
The first author was supported by National Natural Science Foundation of China (11701024), the Fundamental Research Funds for the Central Universities (2019RC17).

DERIVED SEQUENCES AND THE FACTOR SPECTRUM OF THE PERIOD-DOUBLING SEQUENCE

Yuke HUANG¹, Zhiying WEN²

1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2021-03-29 Revised:2021-07-21 Online:2021-12-25 Published:2021-12-27
Supported by:
The first author was supported by National Natural Science Foundation of China (11701024), the Fundamental Research Funds for the Central Universities (2019RC17).

摘要/Abstract

摘要： 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.

关键词: combinatorics on words, envelope word, derived sequence, factor spectrum, reflexivity of derived sequence

Abstract: 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.

Key words: combinatorics on words, envelope word, derived sequence, factor spectrum, reflexivity of derived sequence

中图分类号:

68R15

黄煜可, 文志英. DERIVED SEQUENCES AND THE FACTOR SPECTRUM OF THE PERIOD-DOUBLING SEQUENCE[J]. 数学物理学报(英文版), 2021, 41(6): 1921-1937.

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.

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DERIVED SEQUENCES AND THE FACTOR SPECTRUM OF THE PERIOD-DOUBLING SEQUENCE

DERIVED SEQUENCES AND THE FACTOR SPECTRUM OF THE PERIOD-DOUBLING SEQUENCE

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