Balance properties of Arnoux-Rauzy words

Abstract

The paper deals with balances and imbalances in Arnoux-Rauzy words. We provide sufficient conditions for $C$-balancedness, but our results indicate that even a characterization of 2-balanced Arnoux-Rauzy words on a 3-letter alphabet is not immediate.

References in corpus (2)

• Episturmian words: a survey
• Balance and Abelian complexity of the Tribonacci word

Cited by in corpus (4)

• Geometry, dynamics, and arithmetic of $S$-adic shifts
• Balancedness of Arnoux-Rauzy and Brun words
• Abelian properties of Parry words
• A dynamical view of Tijdeman's solution of the chairman assignment problem