  In a recent series of papers, an exact combinatorial solution was claimed for
a variant of the so-called Marcus--Lushnikov model of aggregation. In this
model, a finite number of aggregates, are initially assumed to be present in
the form of monomers. At each time step, two aggregates are chosen according to
certain size-dependent probabilities and irreversibly joined to form an
aggregate of higher mass. The claimed result given an expression for the full
probability distribution over all possible size distributions in terms of the
so-called Bell polynomials. In this paper, we develop the asymptotics of this
solution in order to check whether the exact solution yields correct
expressions for the average cluster size distribution as obtained from the
Smoluchowski equations. The answer is surprisingly involved: for the generic
case of an arbitrary reaction rate, it is negative, but for the so-called {\em
classical\/} rate kernels, constant, additive and multiplicative, the solutions
obtained are indeed exact. On the other hand, for the multiplicative kernel, a
discrepancy is found in the full solution between the combinatorial solution
and the exact solution. The reasons for this puzzling pattern of agreement and
disagreement are unclear. A better understanding of the combinatorial
solution's derivation is needed, the better to understand its range of
validity.
