An asymptotic Lower Bound for the Maximal Number of Runs in a String

  title={An asymptotic Lower Bound for the Maximal Number of Runs in a String},
  author={Frantisek Franek and Qian Yang},
  journal={Int. J. Found. Comput. Sci.},
An asymptotic lower bound for the maxrun function ρ(n) = max {number of runs in string x | all strings x of length n} is presented. More precisely, it is shown that for any ε > 0, (α−ε)n is an asymptotic lower bound, where α = 3 1+ √ 5 ≈ 0.927. A recent construction of an increasing sequence of binary strings “rich in runs” is modified and extended to prove the result. 

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The maximum number of runs in a string

  • F. Franek, J. Simpson, W. F. Smyth
  • Proc. AWOCA 2003, 14th Australasian Workshop on…
  • 2003
Highly Influential
5 Excerpts

Lower and upper bounds for maximum number of runs

  • Q. Yang
  • M.Sc. thesis, Dept. of Comp. and Software,
  • 2007
1 Excerpt

Some restrictions on Periodicity in Strings

  • S. J. Puglisi, W. F. Smyth, A. Turpin
  • Proc. of AWOCA 2005, 16th Australasian Workshop…
  • 2005
1 Excerpt

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