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arXiv · 2407.19140

Characterizations of Perfectly Clustering Words

Mélodie Lapointe·Christophe Reutenauer
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Abstract

Perfectly clustering words are one of many possible generalizations of Christoffel words. In this article, we propose a factorization of a perfectly clustering word on a $n$ letters alphabet into a product of $n-1$ palindromes with a letter between each of them. This factorization allows us to generalize two combinatorial characterization of Christoffel words due to Pirillo (1999) and de Luca and Mignosi (1994).

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Mélodie Lapointe, Christophe Reutenauer. 2024-07-27. Characterizations of Perfectly Clustering Words. https://arxiv.org/abs/2407.19140

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