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Analytic Combinatorics 1st Edition
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"... 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
The definitive treatment of analytic combinatorics. This self-contained text covers the mathematics underlying the analysis of discrete structures, with thorough treatment of a large number of applications. Exercises, examples, appendices and notes aid understanding: ideal for individual self-study or for advanced undergraduate or graduate courses.
Top customer reviews
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(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!
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.