Word of low complexity without uniform frequencies

Julien Cassaigne (1) , Idrissa Kaboré (2)

1 I2M - Institut de Mathématiques de Marseille
2 UNB - Université Nazi Boni (Bobo-Dioulasso)

In this paper, we construct a uniformely recurrent infinite word of low complexity without uniform frequencies of letters. This shows the optimality of a bound of Boshernitzan, which gives a sufficient condition for a uniformly recurrent infinite word to admit uniform frequencies.

Domaines: Combinatoire [math.CO]

Julien Cassaigne, Idrissa Kaboré. Word of low complexity without uniform frequencies. 2022. ⟨hal-03866716⟩