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On weak circular squares in binary words

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Combinatorial Pattern Matching (CPM 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1264))

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Abstract

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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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, 76100, Rehovot, Israel

    Aviezri S. Fraenkel

  2. School of Mathematics, Curtin University, 6001, Perth, WA, Australia

    Jamie Simpson

  3. Department of Computer Science, University of Warwick, CV4 7AL, Coventry, UK

    Mike Paterson

Authors
  1. Aviezri S. Fraenkel
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  2. Jamie Simpson
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  3. Mike Paterson
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Editor information

Alberto Apostolico Jotun Hein

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© 1997 Springer-Verlag Berlin Heidelberg

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Fraenkel, A.S., Simpson, J., Paterson, M. (1997). On weak circular squares in binary words. In: Apostolico, A., Hein, J. (eds) Combinatorial Pattern Matching. CPM 1997. Lecture Notes in Computer Science, vol 1264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63220-4_51

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  • DOI: https://doi.org/10.1007/3-540-63220-4_51

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63220-7

  • Online ISBN: 978-3-540-69214-0

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