Analytic Combinatorics in Several Variables

The book Analytic Combinatorics in Several Variables by Robin Pemantle, Mark C. Wilson, and Stephen Melczer will be published in 2023 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, as submitted to the publisher, is available here.

The book is undergoing CUP’s printing process and should be available for purchase shortly.

Code

Code working through the examples in this book will be posted here shortly.

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.
• Citations on Google Scholar

Reviews of First Edition

• Robert Sedgewick in Bulletin of the American Mathematical Society (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.”
• Bruce Richmond in 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. "
• Miklos Bona in ACM SIGACT News Vol 45 No 2, 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 in 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 in Choice 51.6 (Feb 2014), 1048: “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.”

Errata for first edition

Owing to an error by the publisher, early copies of the book are missing the list of symbols (which is very important for understanding the book). It can be downloaded from the publisher’s website.

The first edition contains a vast number of typos and other errors that were fixed in the second edition (in addition to new results and an overall simplified presentation). It is highly recommended that readers in 2023 and beyond consult the second edition over the first.