On weak circular squares in binary words

  • Aviezri S. Fraenkel
  • Jamie Simpson
  • Mike Paterson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1264)


A weak square in a binary word is a pair of adjacent nonempty blocks of the same length, having the same number of 1s. A weak circular square is a weak square which is possibly wrapped around the word: the tail protruding from the right end of the word reappears at the left end. Two weak circular squares are equivalent if they have the same length and contain the same number of ones. We prove that the longest word with only k inequivalent weak circular squares contains 4k+2 bits and has the form (01)2k+1 or its complement. Possible connections to tandem repeats in the human genome are pointed out.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Aviezri S. Fraenkel
    • 1
  • Jamie Simpson
    • 2
  • Mike Paterson
    • 3
  1. 1.Department of Applied Mathematics and Computer ScienceWeizmann Institute of ScienceRehovotIsrael
  2. 2.School of MathematicsCurtin UniversityPerthAustralia
  3. 3.Department of Computer ScienceUniversity of WarwickCoventryUK

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