Balance properties of Arnoux-Rauzy words
Val\'erie Berth\'e (LIAFA), Julien Cassaigne (IML), Wolfgang Steiner, (LIAFA)
TL;DR
This paper investigates the balance properties of Arnoux-Rauzy words, providing conditions for their balancedness and highlighting the complexity of characterizing 2-balanced cases on a three-letter alphabet.
Contribution
It offers new sufficient conditions for C-balancedness in Arnoux-Rauzy words and discusses the challenges in fully characterizing 2-balanced instances.
Findings
Provided sufficient conditions for C-balancedness.
Showed that characterizing 2-balanced Arnoux-Rauzy words on 3-letter alphabet is complex.
Indicated that a complete characterization is not straightforward.
Abstract
The paper deals with balances and imbalances in Arnoux-Rauzy words. We provide sufficient conditions for -balancedness, but our results indicate that even a characterization of 2-balanced Arnoux-Rauzy words on a 3-letter alphabet is not immediate.
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