Central and local limit theorems applied to asymptotic enumeration
TLDR
A simple theorem on generating functions is proved which can be used to establish the asymptotic normality of an(k) as a function of k and local limit theorems are turned to in order to obtain asymPTotic formulas for an( k).About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-07-01 and is currently open access. It has received 365 citations till now. The article focuses on the topics: Asymptotic analysis & Asymptotic formula.read more
Citations
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BookDOI
Combinatorial Stochastic Processes
TL;DR: In this paper, the Brownian forest and the additive coalescent were constructed for random walks and random forests, respectively, and the Bessel process was used for random mappings.
Journal ArticleDOI
Singularity analysis of generating functions
Philippe Flajolet,Andrew Odlyzko +1 more
TL;DR: This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymPTotic expansion for the Taylor coefficients of the function.
Book
Average Case Analysis of Algorithms on Sequences
TL;DR: This book provides a unique overview of the tools and techniques used in average case analysis of algorithms.
Book
Asymptotic enumeration methods
TL;DR: In this article, the saddle point and large singularities of analytic functions are used for graphical enumeration, including implicit functions, recurrences, and combinations of methods, which are related to our work.
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Varieties of Increasing Trees
TL;DR: An increasing tree is a labelled rooted tree in which labels along any branch from the root go in increasing order.
References
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Book
Limit Distributions for Sums of Independent Random Variables
B. W. Gnedenko,A. N. Kolmogorov +1 more
Journal ArticleDOI
Stirling Behavior is Asymptotically Normal
TL;DR: The Stirling numbers of the second kind are asymptotically normal as mentioned in this paper, which is similar to results achieved by Feller [1] and Goncarov [2] for other combinatorial distributions.
Journal ArticleDOI
Saddle-point Methods for the Multinomial Distribution
TL;DR: In this article, the authors extend the saddle-point theorem in various directions and give some applications to distributions connected with the multinomial distribution, especially to the distribution of $\chi^2$ and to the maximum entry in a multINomial distribution.