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Limiting distributions for the number of distinct component sizes in relational structures

机译:关系结构中不同组件大小的数量的限制分布

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摘要

We investigate from probabilistic point of view the asymptotic behavior of the number of distinct component sizes in general classes of combinatorial structures of size n as n --> infinity. Mild restrictions of admissibility type are imposed on the corresponding generating functions and asymptotic expressions of the mean and variance of that number are obtained. Then we establish weak convergence to a convolution of two distributions, where one of them is always Gaussian. As an illustration we consider three typical generating function examples: partitions of a finite set, partitions of a positive integer and mappings of a finite set into itself. (C) 1997 Academic Press.
机译:我们从概率的角度研究在n为n->无穷大的组合结构的一般类别中不同分量大小的数量的渐近行为。对相应的生成函数施加适度的可允许性限制,并获得该数的均值和方差的渐近表达式。然后,我们将弱收敛建立为两个分布的卷积,其中之一始终是高斯分布。作为说明,我们考虑三个典型的生成函数示例:有限集的分区,正整数的分区以及有限集到自身的映射。 (C)1997学术出版社。

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