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：
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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.
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页码：305 / 316
页数：11
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