On a Special Class of Primitive Words

  • Authors:

  • Elena Czeizler;Lila Kari;Shinnosuke Seki

  • Affiliations:

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

  • Venue:
  • MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
  • Year:
  • 2008

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Abstract

When representing DNA molecules as words, it is necessary to take into account the fact that a word uencodes basically the same information as its Watson-Crick complement 茂戮驴(u), where 茂戮驴denotes the Watson-Crick complementarity function. Thus, an expression which involves only a word uand 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 茂戮驴-primitive, which cannot be expressed as such repeating sequences. For instance, we prove the existence of a unique 茂戮驴-primitive root of a given word, and we give some constraints forcing two distinct words to share their 茂戮驴-primitive root. Also, we present an extension of the well-known Fine and Wilf Theorem, for which we give an optimal bound.