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Commutation with Ternary Sets of Words

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Abstract

We prove that for any nonperiodic set of words F \subseteq Σ+ with at most three elements, the centralizer of F, i.e., the largest set commuting with F, is F*. Moreover, any set X commuting with F is of the form X = FI, for some I \subseteq ℕ. A boundary point is thus established, as these results do not hold for all languages with at least four words. This solves a conjecture of Karhumäki and Petre, and provides positive answers to special cases of some intriguing questions on commutation of languages, raised by Ratoandromanana and Conway.

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Authors and Affiliations

  1. Department of Mathematics, University of Turku and Turku Centre for Computer Science, Turku 20520, Finland

    Juhani Karhumäki

  2. LIFL, URA CNRS 369, Universite des Sciences et Technologie de Lille, F-59655 Villeneuve d’Ascq, France

    Michel Latteux

  3. Department of Computer Science, Åbo Akademi University and Turku Centre for Computer Science, Turku 20520, Finland

    Ion Petre

Authors
  1. Juhani Karhumäki
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  2. Michel Latteux
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  3. Ion Petre
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Corresponding authors

Correspondence to Juhani Karhumäki, Michel Latteux or Ion Petre.

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Karhumäki, J., Latteux, M. & Petre, I. Commutation with Ternary Sets of Words. Theory Comput Syst 38, 161–169 (2005). https://doi.org/10.1007/s00224-004-1191-1

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  • DOI: https://doi.org/10.1007/s00224-004-1191-1

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