On the abelian complexity of the Rudin-Shapiro sequence

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:451

Article

Lu, Xiaotao¹  Chen, Jin²  Wen, Zhixiong¹  Wu, Wen^3,4 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Huazhong Agr Univ, Coll Sci, Wuhan 430070, Peoples R China

[3] South China Univ Technol, Sch Math, Guangzhou 510641, Guangdong, Peoples R China

[4] Univ Oulu, Math, POB 3000, Oulu 90014, Finland

关键词: Rudin-Shapiro sequence;    Abelian complexity;    k-Regular sequence;    Automatic sequence;    Box dimension;   

DOI  :  10.1016/j.jmaa.2017.02.019

来源: Elsevier

【 摘 要 】

In this paper, we study the abelian complexity of the Rudin Shapiro sequence and a related sequence. We show that these two sequences share the same complexity function p(n), which satisfies certain recurrence relations. As a consequence, the abelian complexity function is 2-regular. Further, we prove that the box dimension of the graph of the asymptotic function lambda(x) is 3/2, where lambda(x) = lim(k ->infinity) rho(4(k)x)/root 4(k)x and rho(x) = p(inverted left perpendicular x inverted right perpendicular) for every x > 0. 9c0 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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