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

2007/01/21 by Boris L. Granovsky, Granovsky, Boris L., Dudley Stark +3 · 1 citation
Mathematics · #05A16 #60C05 #60F05 #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical and Theoretical Analysis #Probability (math.PR) #math.CO #math.PR #msc:05A16 #msc:60C05 #msc:60F05

paper · pdf · doi:10.48550/arxiv.math/0701584

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

openalex publication_date 2007/01/21 · arxiv created 2007/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Log-Concavity and Log-Convexity of Restricted Infinite Products

Related

• Developments in the Khintchine-Meinardus probabilistic method for asymptotic enumeration
• M-partitions: Optimal partitions of weight for one scale pan
• A George Szekeres Formula for Restricted Partitions
• The Size of the Largest Part of Random Weighted Partitions of Large Integers
• Weighted Rogers-Ramanujan Partitions and Dyson Crank