Occurrences of palindromes in characteristic Sturmian words

  • Authors:

  • Amy Glen

  • Affiliations:

  • School of Mathematical Sciences, Discipline of Pure Mathematics, University of Adelaide, South Australia, Australia

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2006

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Abstract

This paper is concerned with palindromes occurring in characteristic Sturmian words cα of slope α, where α ∈ (0, 1) is an irrational. As cα is a uniformly recurrent infinite word, any (palindromic) factor of cαoccurs infinitely many times in cα with bounded gaps. Our aim is to completely describe where palindromes occur in cα. In particular, given any palindromic factor u of cα, we shall establish a decomposition of cα with respect to the occurrences of u. Such a decomposition shows precisely where u occurs in cα, and this is directly related to the continued fraction expansion of α.