Journal:Journal of Mathematical Analysis and Applications

Key Words:Rudin–Shapiro sequence Abelian complexity k-Regular sequence Automatic sequence Box dimension

Abstract: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.

First Author:吕小涛

Indexed by:Journal paper

Discipline:Natural Science

First-Level Discipline:Mathematics

Document Type:J

Volume:451

Page Number:822-838

Translation or Not:no

Date of Publication:2017-01-01

Included Journals:SCI