# An Invitation to Analytic Combinatorics

This is the website for the textbook An Invitation to Analytic Combinatorics: From One to Several Variables by Stephen Melczer (Springer Texts & Monographs in Symbolic Computation).

The book manuscript is available here.

The published version of the textbook can be purchased from the publisher’s website and is available for free through many university libraries via Springer Link. For instance, anyone at Waterloo can obtain the published version for free by clicking this link and logging in with their Waterloo account.

A list of known errata can be found here.

Updates on the theory and applications of Analytic Combinatorics in Several Variables are posted to acsvproject.com.

## Computer Algebra Code for Examples

Each example is encoded as a SageMath Jupyter notebook or Maple worksheet, followed by a static HTML version (which can be viewed on this website, although commands cannot be executed – if you want to run the example yourself make sure to download the code and not the static HTML). An external introduction to SageMath for beginners can run in the browser at this link (or viewed as a static HTML page here).

Some examples (where noted) require the Sage ore_algebra package, the Maple gfun package1, or the Maple Kronecker package. All examples have been tested with Sage 9.2 and Maple 2020.

#### Chapter 1: Introduction

A zip file with everything for Chapter 1 can be downloaded here.

#### Chapter 2: Generating Functions and Analytic Combinatorics

A zip file with everything for Chapter 2 can be downloaded here.

#### Chapter 3: Multivariate Series and Diagonals

A zip file with everything for Chapter 3 can be downloaded here.

An additional Julia worksheet to plot points in contours can be found here.

#### Chapter 4: Lattice Path Enumeration, the Kernel Method, and Diagonals

A zip file with everything for Chapter 4 can be downloaded here.

#### Chapter 5: The Theory of ACSV for Smooth Points

A zip file with everything for Chapter 5 can be downloaded here.

The follow notebook covers Exercises 5.1, 5.2, 5.4–5.7, and 5.9–5.12.
Smooth Point Contributions (Sage code)
Smooth Point Contributions (static HTML)

#### Chapter 6: Lattice Walks and Smooth ACSV

A zip file with everything for Chapter 6 can be downloaded here.

The follow notebook covers Exercises 6.2, 6.3, 6.5, and 6.9.
Highly Symmetric Walk Asymptotics (Sage code)
Highly Symmetric Walk Asymptotics (static HTML)

#### Chapter 7: Automated Analytic Combinatorics

A zip file with everything for Chapter 7 can be downloaded here.

#### Chapters 8, 9 and 10

Code in the process of being finalized.

1. A version of gfun comes built-in to Maple, but better results can often be obtained using the most up-to-date version. The newest version also fixes certain commands which are broken in more recent versions of Maple. ↩︎