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J. C. Fu and W. Y. W. Lou, Distribution Theory of Runs and Patterns and its Applications: A Finite Markov Imbedding Approach, New Jersey: World Scientific, 2003.

has been cited by the following article:

• TITLE: Counting Runs of Ones and Ones in Runs of Ones in Binary Strings

  AUTHORS: Frosso S. Makri, Zaharias M. Psillakis, Nikolaos Kollas

  KEYWORDS: runs; symmetric Bernoulli trials; probability theory; combinatorial problems

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.2 No.4B, January 11, 2013

  ABSTRACT: Consider a binary string (a symmetric Bernoulli sequence) of length . For a positive integer , we exactly enumerate, in all possible binary strings of length , the number of all runs of 1s of length (equal, at least) and the number of 1s in all runs of 1s of length at least . To solve these counting problems, we use probability theory and we obtain simple and easy to compute explicit formulae as well as recursive schemes, for these potential useful in engineering numbers.