On rational structures and their asymptotics

There are many combinatorial structures which can be regarded as complexes of certain basic blocks. Previous results on asymptotic enumeration have yielded implicit formulae for the mean and variance of the counts of blocks, together with Gaussian approximations with these parameters. We will provide explicit formulae for these basic quantities, together with large deviation estimates for decay rates from the mean. As a result we obtain laws of large numbers and, under certain convexity conditions, a new approach to Gaussian approximations previously obtained by more cumbersome analysis.