Counting Runs of Ones and Ones in Runs of Ones in Binary Strings ()

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

Departments of Mathematics and Physics, University of Patras Patras, Greece.

**DOI: **10.4236/ojapps.2012.24B011
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Departments of Mathematics and Physics, University of Patras Patras, Greece.

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.

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Makri, F. , Psillakis, Z. and Kollas, N. (2012) Counting Runs of Ones and Ones in Runs of Ones in Binary Strings. *Open Journal of Applied Sciences*, **2**, 44-47. doi: 10.4236/ojapps.2012.24B011.

Conflicts of Interest

The authors declare no conflicts of interest.

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