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On the Centralizer of a Finite Set

  • Juhani Karhumäki
  • Ion Petre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1853)

Abstract

We prove two results on commutation of languages. First, we show that the maximal language commuting with a three element language, i.e. its centralizer, is rational, thus giving an affirmative answer to a special case of a problem proposed by Conway in 1971. Second, we characterize all languages commuting with a three element code. The characterization is similar to the one proved by Bergman for polynomials over noncommuting variables, cf. Bergman, 1969 and Lothaire, 2000: A language commutes with a three element code X if and only if it is a union of powers of X.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Juhani Karhumäki
    • 1
  • Ion Petre
    • 1
  1. 1.Department of MathematicsUniversity of Turku andTurku Centre for Computer Science (TUCS)TurkuFinland

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