Abstract
It is shown that the distribution of the number of regions r in the random orientable embedding of the graph with one vertex and q loops is approximately proportional to the unsigned Stirling numbers of the first kind s(2 q,r) where r has different parity from q. This approximation is strong enough to imply that both the limiting mean and variance of this distribution differ from ln 2 q by small known constants. The paper concludes with a result on the unimodality of some recursively defined sequences and also some conjectures regarding region distributions of arbitrary graphs.
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