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Uniform Factor-Balancedness in Arnoux-Rauzy Words
Abstract
We characterize uniform factor-balancedness in Arnoux-Rauzy words, generalizing the work of Espinoza, Popoli, and Stipulanti on ternary alphabets to finite alphabets of any size. In particular, we prove that an Arnoux-Rauzy word x is uniformly factor-balanced if and only if x has bounded weak partial quotients.
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BibTeX
@misc{bowley2026uniform,
title = {{Uniform Factor-Balancedness in Arnoux-Rauzy Words}},
author = {Halyna Bowley},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.33919},
eprint = {2609.33919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33919},
}
RIS
TY - UNPB
TI - Uniform Factor-Balancedness in Arnoux-Rauzy Words
AU - Halyna Bowley
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.33919
UR - https://arxiv.org/abs/2609.33919
AB - We characterize uniform factor-balancedness in Arnoux-Rauzy words, generalizing the work of Espinoza, Popoli, and Stipulanti on ternary alphabets to finite alphabets of any size. In particular, we prove that an Arnoux-Rauzy word x is uniformly factor-balanced if and only if x has bounded weak partial quotients.
ER -