Balance properties of Arnoux-Rauzy words

Valérie Berthé (1) , Julien Cassaigne (2) , Wolfgang Steiner (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 IML - Institut de mathématiques de Luminy

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.

Mots clés: infinite words; Arnoux-Rauzy words; balance properties; S-adic sequences

Domaines: Théorie et langage formel [cs.FL]; Combinatoire [math.CO]

Valérie Berthé, Julien Cassaigne, Wolfgang Steiner. Balance properties of Arnoux-Rauzy words. International Journal of Algebra and Computation, 2013, 23 (4), pp.689-704. ⟨10.1142/S0218196713400043⟩. ⟨hal-00767967⟩