Clustering and Arnoux-Rauzy words
Dynamical Systems
2023-05-31 v1
Abstract
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 such that each word of length at least 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.
Cite
@article{arxiv.2305.18986,
title = {Clustering and Arnoux-Rauzy words},
author = {Sébastien Ferenczi and Luca Q. Zamboni},
journal= {arXiv preprint arXiv:2305.18986},
year = {2023}
}