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Beyond the Runs Theorem

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String Processing and Information Retrieval (SPIRE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9309))

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  • International Symposium on String Processing and Information Retrieval

Abstract

In [3], a short and elegant proof was presented showing that a word of length n contains at most \(n-3\) runs. Here we show, using the same technique and a computer search, that the number of runs in a binary word of length n is at most \(\frac{22}{23}n<0.957n\).

Štěpán Holub is supported by the Czech Science Foundation grant number 13-01832S.

J. Fisher and M. Lewenstein are supported by a Grant from the GIF, the German-Israeli Foundation for Scientific Research and Development.

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Author information

Authors and Affiliations

  1. Department of Computer Science, TU Dortmund, Dortmund, Germany

    Johannes Fischer & Tomohiro I

  2. Department of Algebra, Charles University, Praha, Czech Republic

    Štěpán Holub

  3. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Moshe Lewenstein

Authors
  1. Johannes Fischer
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  2. Štěpán Holub
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  3. Tomohiro I
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  4. Moshe Lewenstein
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Corresponding author

Correspondence to Tomohiro I .

Editor information

Editors and Affiliations

  1. King's College London, London, United Kingdom

    Costas Iliopoulos

  2. University of Helsinki, Helsinki, Finland

    Simon Puglisi

  3. University College London, London, United Kingdom

    Emine Yilmaz

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Fischer, J., Holub, Š., I, T., Lewenstein, M. (2015). Beyond the Runs Theorem. In: Iliopoulos, C., Puglisi, S., Yilmaz, E. (eds) String Processing and Information Retrieval. SPIRE 2015. Lecture Notes in Computer Science(), vol 9309. Springer, Cham. https://doi.org/10.1007/978-3-319-23826-5_27

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  • DOI: https://doi.org/10.1007/978-3-319-23826-5_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23825-8

  • Online ISBN: 978-3-319-23826-5

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