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arXiv · 2302.09626

Bracket words along Hardy field sequences

Jakub Konieczny·Clemens Müllner
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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.

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Jakub Konieczny, Clemens Müllner. 2023-02-19. Bracket words along Hardy field sequences. https://doi.org/10.1017/etds.2023.112

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