On Convergence Rates in the Central Limit Theorems for Combinatorial Structures

Flajolet and Soria established several central limit theorems for the parameter ‘number of components’ in a wide class of combinatorial structures. In this paper, we shall prove a simple theorem which applies to characterize the convergence rates in their central limit theorems. This theorem is also applicable to arithmetical functions. Moreover, asymptotic expressions are derived for moments of integral order. Many examples from different applications are discussed.