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arXiv · 2305.18986

Clustering and Arnoux-Rauzy words

Sébastien Ferenczi·Luca Q. Zamboni
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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 $K$ 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.

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Sébastien Ferenczi, Luca Q. Zamboni. 2023-05-30. Clustering and Arnoux-Rauzy words. https://arxiv.org/abs/2305.18986

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