Counting Runs of Ones and Ones in Runs of Ones in Binary Strings
Frosso S. Makri, Zaharias M. Psillakis, Nikolaos K. Kollas · Open Journal of Applied Sciences · 2012
Consider a binary string (a symmetric Bernoulli sequence) of length �.For a positive integer �, 1 ≤ � ≤ �, we exactly enumerate, in all 2 � 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.