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Perfectly Clustering Words are Primitive Positive Elements of the Free Group

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Combinatorics on Words (WORDS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12847))

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Abstract

A word over a totally ordered alphabet is perfectly clustering if its Burrows-Wheeler transform is a non-increasing word. A famous example of a family of perfectly clustering words are Christoffel words and their conjugates. In this paper, we show another similarity between perfectly clustering words and Christoffel words: Both are positive primitive elements of the free group.

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Acknowledgments

We would like to thank Christophe Reutenauer and Valérie Berthé for their suggestions and their helpful comments. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number BP–545242–2020], and the Fonds de recherche du Québec – Nature et Technologies (FRQNT).

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Authors and Affiliations

  1. Université de Paris, IRIF, CNRS, 75006, Paris, France

    Mélodie Lapointe

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  1. Mélodie Lapointe
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Correspondence to Mélodie Lapointe .

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Editors and Affiliations

  1. University of Rouen Normandy, Mont-St-Aignan, France

    Thierry Lecroq

  2. Saint Petersburg State University, Saint Petersburg, Russia

    Svetlana Puzynina

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Lapointe, M. (2021). Perfectly Clustering Words are Primitive Positive Elements of the Free Group. In: Lecroq, T., Puzynina, S. (eds) Combinatorics on Words. WORDS 2021. Lecture Notes in Computer Science(), vol 12847. Springer, Cham. https://doi.org/10.1007/978-3-030-85088-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-85088-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85087-6

  • Online ISBN: 978-3-030-85088-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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