Analytic Combinatorics in Several Variables

The book Analytic Combinatorics in Several Variables, 2nd Edition by Robin Pemantle, Mark C. Wilson, and Stephen Melczer will be published in February 2024 by Cambridge University Press. The book is aimed at researchers in analytic combinatorics, and fields in which enumerative questions arise that can be solved by the methods of analytic combinatorics.

The manuscript for the second edition is available for download here.

Available for purchase on the publisher website.

An updating errata list is available here.

Code

Completed Sage notebooks are below – notebooks for the rest of the text are in progress and will be posted below when available.

These notebooks have been tested on SageMath 10.1 but should work with any recent version of Sage. A brief introduction to Sage can be viewed or downloaded here. To download the Jupyter notebooks you may need to right-click on the links.

Chapter 1: Jupyter notebook or static HTML
Chapter 2: Jupyter notebook or static HTML
Chapter 3: Jupyter notebook or static HTML
Chapter 4: Jupyter notebook or static HTML
Chapter 5: no notebook for this chapter
Chapter 6: in progress
Chapter 7: no notebook for this chapter
Chapter 8: in progress
Chapter 9: in progress
Chapter 10: in progress
Chapter 11: in progress
Chapter 12: in progress

Reviews

For the Second Edition

Richard P. Stanley: “A definitive treatment of a challenging but very useful subject. There is a wide variety of situations calling for the estimation of the coefficients of a multivariate generating function. The authors have done a superb job of classifying and elucidating the myriad of available techniques for achieving this aim.”
Robert Sedgewick: “This book is an invaluable resource that is certain to have dramatic impact on research and teaching in this rapidly developing area of mathematics. The first edition broke new ground; this edition prepares the field for others to harvest new knowledge with important applications in many scientific disciplines.”

For the First Edition

Bruce Richmond (Mathematical Reviews): “This book is a timely and well-written description of contemporary multivariate analytic combinatorics, and the authors deserve much credit for the progress since 1995. The book is written as a text with helpful exercises to illuminate the concepts; students will see several branches of modern mathematics and computer algebra interact. "
Robert Sedgewick (Bulletin of the AMS, July 2018): “The organization of the book is exemplary … The treatment of analytic methods for multivariate generating functions in this book is breathtaking … Whether or not one cares about applications, this book is an extremely well- written treatment of a relevant contemporary topic that many mathematicians will see as an opportunity to learn and appreciate new areas of mathematics and how they interact.”
Miklos Bona (ACM SIGACT News, 2014): “It should be clear from all the above that there is no other book on the market that comes remotely close to this one.”
Michael Albert (New Zealand Mathematical Society Newsletter, Dec 2013): “Since roughly the turn of this century the authors have been at the forefront of the development of more general, less ad hoc, techniques for such and related problems. This book develops, summarises and illustrates the results of their work both theoretically and in practice. As such, it fills a gap that was very much in need of filling.” … “I for one am very grateful to have it on my desk now.”
D.V. Feldman (Choice 51.6, Feb 2014): “Few books ever made a better case for the grand unity of mathematics.” … “It deserves a place on college library shelves even if nearly all undergraduates will find it too daunting, for it provides a nearly universal answer to the ‘what can I do with this stuff?’ question that students pose in so many basic courses. Recommended.”

First Edition

The first edition of the book was published in 2013.

Published version (see also Amazon).
First draft sent to Cambridge University Press in November 2012.