Analytic Combinatorics

@inproceedings{Flajolet2009AnalyticC,
  title={Analytic Combinatorics},
  author={Philippe Flajolet and Robert Sedgewick},
  year={2009}
}
Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text… 
Analytic Combinatorics in Several Variables
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An invitation to analytic combinatorics and lattice path counting
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Workshop in Analytic and Probabilistic Combinatorics BIRS-16w5048
  • M. Bóna
  • Mathematics, Computer Science
  • 2016
TLDR
Applied problems of interest are drawn from classic combinatorics, graph theory, information theory, number theory, probability, theoretical computer science, and applied areas, including biological sciences, information sciences, mathematical and statistical physics, and so on.
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References

SHOWING 1-10 OF 524 REFERENCES
Basic analytic combinatorics of directed lattice paths
Analytic combinatorics of non-crossing configurations
Mathematics for the analysis of algorithms (2nd ed.)
TLDR
This monograph, taken from an advanced course at Stanford, covers binomial identities, recurrence relations, operator methods, and asymptotic analysis, and the subject of hashing is explored via operator methods.
An Introduction to Combinatory Analysis
IN this little book Major P. A. MacMahon has given a short introduction to his two volumes on combinatory analysis which were published in 1915–16. The theories of combination, permu tation,
Resurrecting the asymptotics of linear recurrences
Combinatorial species and tree-like structures
The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the
Logarithmic Combinatorial Structures: A Probabilistic Approach
The elements of many classical combinatorial structures can be naturally decomposed into components. Permutations can be decomposed into cycles, polynomials over a finite field into irreducible
Airy Phenomena and Analytic Combinatorics of Connected Graphs
TLDR
It is shown here that it is possible to make analytic sense of the divergent series that expresses the generating function of connected graphs and derive analytically known enumeration results using only first principles of combinatorial analysis and straight asymptotic analysis—specifically, the saddle-point method.
A Logical Approach to Asymptotic Combinatorics
We shall present a general framework for dealing with an extensive set of problems from asymptotic combinatorics; this framework provides methods for determining the probability that a large, finite
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