Clustering and Arnoux-Rauzy words

Sébastien Ferenczi (1) , Luca Q Zamboni (2)

1 I2M - Institut de Mathématiques de Marseille
2 ICJ - Institut Camille Jordan

We characterize the clustering of a word under the Burrows-Wheeler transform in terms of the resolution of a bounded number of bispecial factors belonging to the language generated by all its powers. We use this criterion to compute, in every given Arnoux-Rauzy language on three letters, an explicit bound K such that each word of length at least K is not clustering; this bound is sharp for a set of Arnoux-Rauzy languages including the Tribonacci one. In the other direction, we characterize all standard Arnoux-Rauzy clustering words, and all perfectly clustering Arnoux-Rauzy words. We extend some results to episturmian languages, characterizing those which produce infinitely many clustering words, and to larger alphabets.

Domaines: Mathématiques [math]

Sébastien Ferenczi, Luca Q Zamboni. Clustering and Arnoux-Rauzy words. Advances in Applied Mathematics, 2023, 153, pp.102621. ⟨10.1016/j.aam.2023.102621⟩. ⟨hal-04276825⟩