# 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…

## 3,030 Citations

Analytic Combinatorics in Several Variables

- Mathematics
- 2013

This book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective. Analytic combinatorics is a branch of enumeration that uses analytic techniques to…

An invitation to analytic combinatorics and lattice path counting

- Mathematics
- 2015

The term “Analytic Combinatorics”, coined by P. Flajolet and B. Sedgewick [6], combines powerful analytic methods from complex analysis with the field of enumerative combinatorics. The link between…

Algorithms for Analytic Combinatorics – PI 4 Program 2018

- Computer Science
- 2018

This program will study the use of analytic techniques and their wide range of applications across several disciplines, with a focus on implementing algorithms which will be of use to current and future researchers.

Analytic combinatorics: a calculus of discrete structures

- Computer Science, MathematicsSODA '07
- 2007

This work surveys methods of analytic combinatorics that are simply based on the idea of associating numbers to atomic elements that compose combinatorial structures, then examining the geometry of the resulting functions, and emerges an operational calculus of discrete structures.

Computer Algebra in the Service of Enumerative Combinatorics

- MathematicsISSAC
- 2021

An overview of recent results on structural properties and explicit formulas for generating functions of walks with small steps in the quarter plane are given, especially two important paradigms: "guess-and-prove" and "creative telescoping".

Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables

- MathematicsISSAC
- 2016

Effective algorithms required for the study of analytic combinatorics in several variables, together with their complexity analyses are provided.

Lattice walks at the Interface of Algebra, Analysis and Combinatorics

- Mathematics
- 2018

Lattice paths are a classic object of mathematics, with applications in a wide range of areas including combinatorics, theoretical computer science and queuing theory. In the past ten years, several…

Combinatorial Adventures in Analysis, Algebra, and Topology

- Mathematics
- 2020

The authors of this piece are organizers of the AMS 2020 Mathematics Research Communities summer conference Combinatorial Applications of Computational Geometry and Algebraic Topology, one of five…

Asymptotics of lattice walks via analytic combinatorics in several variables

- Mathematics
- 2015

International audience
We consider the enumeration of walks on the two-dimensional non-negative integer lattice with steps defined by a finite set S ⊆ {±1, 0}2 . Up to isomorphism there are 79…

Workshop in Analytic and Probabilistic Combinatorics BIRS-16w5048

- Mathematics, Computer Science
- 2016

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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