Thue-Morse-Sturmian words and critical bases for ternary alphabets
Dynamical Systems
2019-02-20 v1 Number Theory
Abstract
The set of unique -expansions over the alphabet is trivial for below the golden ratio and uncountable above the Komornik-Loreti constant. Generalisations of these thresholds for three-letter alphabets were studied by Komornik, Lai and Pedicini (2011, 2017). We use S-adic words including the Thue-Morse word (which defines the Komornik-Loreti constant) and Sturmian words (which characterise generalised golden ratios) to determine the value of a certain generalisation of the Komornik-Loreti constant to three-letter alphabets.
Keywords
Cite
@article{arxiv.1902.07078,
title = {Thue-Morse-Sturmian words and critical bases for ternary alphabets},
author = {Wolfgang Steiner},
journal= {arXiv preprint arXiv:1902.07078},
year = {2019}
}