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1 results

  • On automatic infinite permutations∗

  • Anna Frid, Luca Zamboni
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 46 / Issue 1 / January 2012
    Published online by Cambridge University Press:
    23 November 2011, pp. 77-85
    Print publication:
    January 2012

  • An infinite permutation α is a linear ordering of N. We study propertiesof infinite permutations analogous to those of infinite words, and show some resemblancesand some differences between permutations and words. In this paper, we try to extend topermutations the notion of automaticity. As we shall show, the standard definitions whichare equivalent in the case of words are not equivalent in the context of permutations. Weinvestigate the relationships between these definitions and prove that they constitute achain of inclusions. We also construct and study an automaton generating the Thue-Morsepermutation.