International Symposium on String Processing and Information Retrieval

SPIRE 2015: String Processing and Information Retrieval pp 277-286 | Cite as

Beyond the Runs Theorem

  • Johannes Fischer
  • Štěpán Holub
  • Tomohiro I
  • Moshe Lewenstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9309)


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 \(\frac{22}{23}n<0.957n\).


Runs Lyndon words Combinatorics on words 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Johannes Fischer
    • 1
  • Štěpán Holub
    • 2
  • Tomohiro I
    • 1
  • Moshe Lewenstein
    • 3
  1. 1.Department of Computer ScienceTU DortmundDortmundGermany
  2. 2.Department of AlgebraCharles UniversityPrahaCzech Republic
  3. 3.Department of Computer ScienceBar-Ilan UniversityRamat GanIsrael

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