On the Repetition Threshold for Large Alphabets

  • Arturo Carpi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)

Abstract

The (maximal) exponent of a finite non-empty word is the ratio among its length and its period. Dejean (1972) conjectured that for any n ≥5 there exists an infinite word over n letters with no factor of exponent larger than n/(n–1). We prove that this conjecture is true for n ≥38.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Arturo Carpi
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di PerugiaItaly

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