TITLE:
Some New Results on the Number of Paths
AUTHORS:
Beih S. El-Desouky, Abdelfattah Mustafa, E. M. Mahmoud
KEYWORDS:
Stirling Numbers, Generating Function, Moment Generating Function, Comtet Numbers, Maple Program
JOURNAL NAME:
Open Journal of Modelling and Simulation,
Vol.3 No.3,
June
5,
2015
ABSTRACT: Khidr and El-Desouky [1] derived a symmetric sum involving the Stirling numbers of the first kind through the process of counting the number of paths along a rectangular array n*m denoted by Anm. We investigate the generating function for the general case and hence some special cases as well. The probability function of the number of paths along is obtained. Moreover, the moment generating function of the random variable X and hence the mean and variance are obtained. Finally, some applications are introduced.