English

Bracket words along Hardy field sequences

Number Theory 2024-11-20 v1 Combinatorics Dynamical Systems

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 nc\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.

Keywords

Cite

@article{arxiv.2302.09626,
  title  = {Bracket words along Hardy field sequences},
  author = {Jakub Konieczny and Clemens Müllner},
  journal= {arXiv preprint arXiv:2302.09626},
  year   = {2024}
}

Comments

26 pages, comments welcome

R2 v1 2026-06-28T08:43:54.788Z