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- W1583577088 abstract "Let $c_{m,n}$ be the number of weighted partitions of the positive integer $n$ with exactly $m$ parts, $1le mle n$. For a given sequence $b_k, kge 1,$ of part type counts (weights), the bivariate generating function of the numbers $c_{m,n}$ is given by the infinite product $prod_{k=1}^infty(1-uz^k)^{-b_k}$. Let $D(s)=sum_{k=1}^infty b_k k^{-s}, s=sigma+iy,$ be the Dirichlet generating series of the weights $b_k$. In this present paper we consider the random variable $xi_n$ whose distribution is given by $P(xi_n=m)=c_{m,n}/(sum_{m=1}^nc_{m,n}), 1le mle n$. We find an appropriate normalization for $xi_n$ and show that its limiting distribution, as $ntoinfty$, depends on properties of the series $D(s)$. In particular, we identify five different limiting distributions depending on different locations of the complex half-plane in which $D(s)$ converges." @default.
- W1583577088 created "2016-06-24" @default.
- W1583577088 creator A5012982414 @default.
- W1583577088 date "2011-10-24" @default.
- W1583577088 modified "2023-10-01" @default.
- W1583577088 title "Limit Theorems for the Number of Parts in a Random Weighted Partition" @default.
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- W1583577088 doi "https://doi.org/10.37236/693" @default.
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