Analytic Combinatorics

  title={Analytic Combinatorics},
  author={Philippe Flajolet and Robert Sedgewick},
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
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
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
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
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
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
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
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
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
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
  • M. Bóna
  • 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.


Basic analytic combinatorics of directed lattice paths
Analytic combinatorics of non-crossing configurations
Mathematics for the analysis of algorithms (2nd ed.)
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
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