A Monte Carlo method for series expansions

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Abstract
The authors describe a simple and general algorithm to calculate series expansions in enumeration problems to large orders approximately by a Monte Carlo method. It can be used to generate unbiased samples in cluster studies, e.g. linear or branched polymers, random surfaces, etc., in any dimension. They calculate the number of site animals of size n on the square lattice for n <or= 50 and their average size to better than 1% accuracy.