发表刊物：Journal of Mathematical Analysis and Applications

关键字：Rudin–Shapiro sequence Abelian complexity k-Regular sequence Automatic sequence Box dimension

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 ρ(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 λ(x)is 3/2, where λ(x) =limk→∞ρ(4kx)/√4kxand ρ(x) =ρ(x)for every x >0.

第一作者：吕小涛

论文类型：期刊论文

学科门类：理学

一级学科：数学

文献类型：J

卷号：451

页面范围：822-838

是否译文：否

发表时间：2017-01-01

收录刊物：SCI