On a special class of primitive words

  • Authors:

  • Elena Czeizler;Lila Kari;Shinnosuke Seki

  • Affiliations:

  • Department of Computer Science, The University of Western Ontario, London, Ontario, N6A 5B7, Canada;Department of Computer Science, The University of Western Ontario, London, Ontario, N6A 5B7, Canada;Department of Computer Science, The University of Western Ontario, London, Ontario, N6A 5B7, Canada

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

When representing DNA molecules as words, it is necessary to take into account the fact that a word u encodes basically the same information as its Watson-Crick complement @q(u), where @q denotes the Watson-Crick complementarity function. Thus, an expression which involves only a word u and its complement can be still considered as a repeating sequence. In this context, we define and investigate the properties of a special class of primitive words, called pseudo-primitive words relative to @q or simply @q-primitive words, which cannot be expressed as such repeating sequences. For instance, we prove the existence of a unique @q-primitive root of a given word, and we give some constraints forcing two distinct words to share their @q-primitive root. Also, we present an extension of the well-known Fine and Wilf theorem, for which we give an optimal bound.