Meinardus' theorem on weighted partitions: extensions and a probabilistic proof

Details Meinardus' theorem on weighted partitions: extensions and a probabilistic proof Meinardus' theorem on weighted partitions: extensions and a probabilistic proof

2007-01-21

arxiv.org/abs/math/0701584v2

Mathematics

Probability

The version contains a few minor corrections.It will be published in Advances in Applied Mathematics

Scientific paper

We give a probalistic proof of the famous Meinardus' asymptotic formula for the number of weighted partitions with weakened one of the three Meinardus' conditions, and extend the resulting version of the theorem to other two classis types of decomposable combinatorial structures, which are called assemblies and selections. The results obtained are based on combining Meinardus' analytical approach with probabilistic method of Khitchine.

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