q-Series Arising From The Study of Random Graphs

This paper deals with q-series arising from the study of the transitive closure problem in random acyclic digraphs. In particular, it presents an identity involving divisor generating functions which allows us to determine the asymptotic behavior of polynomials defined by a general class of recursive equations, including the polynomials for the mean and the variance of the size of the transitive closure in random acyclic digraphs.