Critical Exponents of Regular Arnoux-Rauzy Sequences

Download PDF
Open Webpage

L'ubomíra Dvoráková, Jana Lepsová

Published: 01 Jan 2023, Last Modified: 15 May 2025WORDS 2023EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We provide a formula for the critical exponent and the asymptotic critical exponent of regular Arnoux-Rauzy sequences. Over the binary alphabet it coincides with a well-known formula for Sturmian sequences based on their S-adic representation. We show that among regular d-ary Arnoux-Rauzy sequences, the minimal (asymptotic) critical exponent is reached by the d-bonacci sequence.