On the Maximal Multiplicity of Parts in a Random Integer Partition

被引：0

作者：

Ljuben R. Mutafchiev

机构：

[1] American University in Bulgaria,Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences

来源：

The Ramanujan Journal | 2005年 / 9卷

关键词：

integer partitions; multiplicity of parts; limiting distributions;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the asymptotic behavior of the maximal multiplicity μn = μn(λ) of the parts in a partition λ of the positive integer n, assuming that λ is chosen uniformly at random from the set of all such partitions. We prove that πμn/(6n)1/2 converges weakly to max jXj/j as n→∞, where X1, X2, … are independent and exponentially distributed random variables with common mean equal to 1.

引用

页码：305 / 316

页数：11

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