Factor versus palindromic complexity of uniformly recurrent infinite words

  • Authors:

  • Peter Balái;Zuzana Masáková;Edita Pelantová

  • Affiliations:

  • Department of Mathematics, FNSPE, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czech Republic;Department of Mathematics, FNSPE, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czech Republic;Department of Mathematics, FNSPE, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czech Republic

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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Abstract

We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n)+P(n+1)@?@DC(n)+2, for all n@?N. For a large class of words this is a better estimate of the palindromic complexity in terms of the factor complexity than the one presented in [J.-P. Allouche, M. Baake, J. Cassaigne, D. Damanik, Palindrome complexity, Theoret. Comput. Sci. 292 (2003) 9-31]. We provide several examples of infinite words for which our estimate reaches its upper bound. In particular, we derive an explicit prescription for the palindromic complexity of infinite words coding r-interval exchange transformations. If the permutation @p connected with the transformation is given by @p(k)=r+1-k for all k, then there is exactly one palindrome of every even length, and exactly r palindromes of every odd length.