Bracket words along Hardy field sequences

Abstract

We study bracket words, which are a far-reaching generalisation of Sturmian words, along Hardy field sequences, which are a far-reaching generalisation of Piatetski--Shapiro sequences $\lfloor n^c\rfloor$. We show that thus obtained sequences are deterministic (i.e., they have sub-exponential subword complexity) and satisfy Sarnak's conjecture.

26 pages, comments welcome

References in corpus (3)

• Higher uniformity of arithmetic functions in short intervals I. All intervals
• Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences
• Synchronizing automatic sequences along Piatetski-Shapiro sequences