Palindrome complexity

  • Authors:

  • Jean-Paul Allouche;Michael Baake;Julien Cassaigne;David Damanik

  • Affiliations:

  • CNRS, LRI, Université Paris-Sud, (Paris XI), Bât. 490, F-91405 Orsay Cedex, France;Institut für Mathematik und Informatik, Universität Greifswald, Jahnstraße 15 a, D-17487 Greifswald, Germany;CNRS, IML Case 907, 163 Avenue de Luminy, F-13288 Marseille, Cedex 9, France;Department of Mathematics 253-37, California Institute of Technology, Pasadena, CA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

We study the palindrome complexity of infinite sequences on finite alphabets, i.e., the number of palindromic factors (blocks) of given length occurring in a given sequence. We survey the known results and obtain new results for some sequences, in particular for Rote sequences and for fixed points of primitive morphisms of constant length belonging to "class P" of Hof-Knill-Simon. We also give an upper bound for the palindrome complexity of a sequence in terms of its (block-)complexity.