Combinatorics, Probability and Computing a General Asymptotic Scheme for the Analysis of Partition Statistics a General Asymptotic Scheme for the Analysis of Partition Statistics
Combinatorics, Probability and Computing a General Asymptotic Scheme for the Analysis of Partition Statistics a General Asymptotic Scheme for the Analysis of Partition Statistics
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组合学、概率和计算 分区统计分析的一般渐近方案 分区统计分析的一般渐近方案
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通讯作者：
S. Wagner
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P. J. Grabner;A. Knopfmacher;S. Wagner;A. General;P. J. Grabner;A. Knopfmacher;S. Wagner
致力于内存的菲利普Flajolet我们认为统计性质的随机整数分区。为了计算各种划分统计量的均值、方差和高阶矩，人们经常必须研究形式为P（x）F（x）的生成函数，其中P（x）是划分数量的生成函数。在本文中，我们展示了如何渐近展开可以得到一个准自动的方式从F（x）的x = 1，这平行于经典的奇异性分析的Flajolet和Odlyzko在许多方面的展开。从文献中的许多例子，以及一些新的统计数据，通过这种方法进行处理。此外，我们将展示如何计算进一步的条款在以前研究的分区统计的渐近展开。图1.图9 + 7 + 5 + 5 + 2 + 1 + 1 + 1和一些分区统计。
Dedicated to the memory of Philippe Flajolet We consider statistical properties of random integer partitions. In order to compute means, variances and higher moments of various partition statistics, one often has to study generating functions of the form P (x)F(x), where P (x) is the generating function for the number of partitions. In this paper, we show how asymptotic expansions can be obtained in a quasi-automatic way from expansions of F(x) around x = 1, which parallels the classical singularity analysis of Flajolet and Odlyzko in many ways. Numerous examples from the literature, as well as some new statistics, are treated via this methodology. In addition, we show how to compute further terms in the asymptotic expansions of previously studied partition statistics. Figure 1. The Ferrers diagram of the partition 9 + 7 + 5 + 5 + 2 + 1 + 1 + 1 and some partition statistics.