Analytic Combinatorics

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.

Este libro es un clásico, pero está impreso con una calidad horrible, letras apenas legibles tanto por el tamaño como por la falta de contraste. Una pena, porque pensé que sería un plus tenerlo impreso. Me costó caro tanto el libro como su envío, una decepción total.

nice book

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.

Sort of the hidden underbelly of combinatorial mathematics is the relationship to fractals and this book actually seems to admit it exists. Some of the different types of generating function are hard to follow and a reference to Roman's Umbral calculus or Sheffer sequences would be useful as well, but a lot of very useful information is here and they do mention Dr. Sloane's EIS. Not since I got a look at the classic Riordan text have I seen a book that packs this kind of impact on the field of combinatorial mathematics. This book is one for students who are serious about learning the developing science of combinatorial analysis. I just wish I could afford it and not have to check it out of the library to be able to read it! The connection of Bernoulli functions to bosons and 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.

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

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.

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.