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.