Fine and Wilf’s Theorem and Pseudo-repetitions

  • Florin Manea
  • Robert Mercaş
  • Dirk Nowotka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


The notion of repetition of factors in words is central to considerations on sequences. One of the recent generalizations regarding this concept was introduced by Czeizler et al. (2010) and investigates a restricted version of that notion in the context of DNA computing and bioinformatics. It considers a word to be a pseudo-repetition if it is the iterated concatenation of one of its prefixes and the image of this prefix through an involution. We present here a series of results in the fashion of the Fine and Wilf Theorem in a more general setting where we consider the periods of some word given by a prefix of it and images of that prefix through some arbitrary morphism or antimorphism.


Natural Number Cyclic Permutation Great Common Divisor Proper Factor Biological Motivation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Florin Manea
    • 1
  • Robert Mercaş
    • 2
  • Dirk Nowotka
    • 1
  1. 1.Institut für InformatikChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Fakultät für InformatikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

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