Article citationsMore>>

M. V. Koutras, “Applications of Markov chains to the distribution theory of runs and patterns,” in Handbook of Statistics, vol. 21, D. N. Shanbhag, C. R. Rao, Eds. North Holland: Elsevier, 2003, pp. 431-472.

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.