Analytic Combinatorics by Philippe Flajolet (PDF)

Description

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 is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

User’s Reviews

Editorial Reviews: Review “… this is a valuable, comprehensive treatment.” Angele M. Hamel, reviews.com”… certain to become the standard reference book of the field. While Analytical Combinatorics has more than enough information to become a reference book, it is also written in a reader-friendly style that makes it appropriate as a course resource. In the past, it was not always clear what “analytic combinatorics” meant; this book will bring about a consensus on that question.” M. Bona, Choice Magazine”Because of the breadth, and depth of topical coverage, the highly applicable results and the enjoyable writing that characterize this book, Analytic Combinatorics is now defined. The authors wrote the book on it.” Miklos Bona, SIGNACT News Book Description The definitive treatment of analytic combinatorics, from leaders in the field. Exercises, examples, appendices and notes aid understanding. About the Author Philippe Flajolet is Research Director of the Algorithms Project at INRIA Rocquencourt.Robert Sedgewick is William O. Baker Professor of Computer Science at Princeton University, New Jersey. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book covers a LOT of ground FAST. You can think of it as the third volume in the following sequence:(1) Algorithms; Sedgewick and Wayne. Appropriate for an upper level undergrad/grad text book for a university algorithms course.(2) Analysis of Algorithms; Sedgewick and Flajolet. Much more detailed treatment of algorithms, and using the Generating Function approach to Algorithm Analysis.(3) Analytic Combinatorics: S&J. Advanced aspects of the above.Here is the setup: For some category of computer science or combinatorical object, let A[n] denote how many distinct examples there are of size n. Then the complex function f(z) = sum(A[n] z^n) is the “Generating function” for A[n].The S&J methodology is (1) generate an equation for f(z) directly from the combinatorical object. (2) Use this equation to solve for f(z), or at least obtain info about it. (3) Use classical complex analysis (singularity analysis and saddle point methods) to obtain excellent estimates of A[n].I am confident this will get easy once I work out about 100 examples!

⭐Flajolet and his group at INRIA (B. Salvy, P. Zimmermann, many others) have created the field of “analytic combinatorics”, and this book has everything you might possibly want to know about the subject (since the selection of topics is very thoughtful, it does not have that much you would NOT want to know). The only reason to possibly not get this book (assuming you are interested in the subject) is that the PDF is available free on Flajolet’s web page, but the book for is quite convenient and quite reasonably priced.

⭐nice book

⭐Sort of the hidden underbelly of combinatorial mathematics is the relationship tofractals and this book actually seems to admit it exists.Some of the different types of generating function are hard to followand a reference to Roman’s Umbral calculus or Sheffer sequenceswould be useful as well, but a lot of very useful informationis here and they do mention Dr. Sloane’s EIS.Not since I got a look at the classic Riordan text have I seena book that packs this kind of impact on the fieldof combinatorial mathematics.This book is one for students who are serious about learningthe developing science of combinatorial analysis.I just wish I could afford itand not have to check it out of the library to be able to read it!The connection of Bernoulli functions to bosonsand Euler functions to leptons isn’t touched on,but it is the reason that combinatorial analysis is important to physics.So you can’t give the book 5 stars even as good as what is presented is.

⭐Wow!!! I would have thought the plans to build Combinaoric transformer robots would be classified but here is all the theory on Amazon. Whoa?!? My wife got me this as a 25th anniversary present and I thought that’s not so romantic but I couldn’t have been more wrong. We’ve both read this book cover to cover a few times and it is hot stuff. I hope you live someplace cold because you will not want to go out until spring after you get this pot boiler cooking.

⭐Concrete methods for a modern approach to actually analyzing algorithms for practical purposes. Lots of theory, but that theory is applied to get you the answers you need.

⭐excellent book for people interested in heading beyong the combinatorics of texts and reaching to the research level combinatorics.

⭐Zero stars if i could have selected that. Basically, this is a ripoff. From the amazon metadata, you are led to believe it is a 2014 version, but what you get is a 2004 draft. Adding insult to injury, the publisher decided that it would be a good idea to have 2 inch left, right and bottom margins for this book.

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