A General Asymptotic Scheme for Moments of Partition Statistics

Abstract. In order to compute means, variances and higher moments of various partition statistics, one often has to study generating functions of the form P (x)F (x), where P (x) is the generating function for the number of partitions. In this paper, we show how asymptotic expansions can be obtained in a quasi-automatic way from expansions of F (x) around x = 1. Numerous examples from the literature, as well as some new statistics are treated via this methodology. In addition, we show how to compute further terms in the asymptotic expansions of previously studied partition statistics.