S (01) Article electronically published on October 12, Enumerative combinatorics, Volume 2, by Richard P. Stanley, Cambridge Univer . Both volumes already had pages on MAA Reviews, because both appeared in the a common assumption, because one now finds a note on Stanley’s web site indicating that “there will be no second edition of Volume 2. Volume 1 of Enumerative Combinatorics was published by Wadsworth Volumes 1 and 2 can be ordered online from Cambridge University Press ( volume 1.

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Enumerative Combinatorics: Volume 2

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Would you like to tell us about a lower price? This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions.

The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory.

An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

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A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory. Editorial Reviews Review ” Both volumes highly recommended for all libraries. Stanley’s book is a valuable contribution to enumerative combinatorics. Beginners will find it an accessible introduction to the subject, and experts will still find much to learn from it.

This is the second volume of a two-volume work on the subject of enumerative combinatorics, an area of mathematics with connections to many other topics within and outside of wnumerative, such as computer science, spectroscopy, algebraic geometry, algebraic topology, and representation theory. Many topics covered in particular, the theory of symmetric functions are not available in any other textbook at this level, and the usefulness of the book is enhanced by over exercises with solutions.

Although primarily intended as a textbook for graduate students and a resource for professional mathematicians, some parts of the book will be accessible to mathematics undergraduates and even interested enunerative. See all Editorial Reviews. Product details File Size: Up to 4 simultaneous devices, per publisher limits Publisher: January 13, Sold by: Share your thoughts with other customers. Write a customer review.


Showing of 12 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later. Excellent book but very dense. Not meant for the novice, and sttanley very hard read for even the intermediate. This book is meant to be “read” with pencil and paper in hand. The presentation clearly comes from enu,erative author enumeratve just loves to “count”, and is an expert at it. The clarity of thought is appreciated. Some will appreciate the conciseness, others might wish for a little more explanation.

The coverage is exhaustive and the book can also serve as a enumdrative. This is an excellent book on combinatorics, but it is quite difficult to understand–written for experts, not novices. The author often chooses a more general framework in which to present things, and this can make the material quite difficult to follow.

But the rewards for the diligent reader are great. Occasionally I question how Stanley chooses to present a certain topic, but usually if I look closely enough, I see that there are deep reasons for his choice of notation or presentation. Some of the material in this book is dombinatorics than others; some stanely it depends on earlier chapters, but some stands on its own.

People interested in partially ordered sets and lattices may want to jump ahead to that chapter–much of this chapter stands on its own, and it is an excellent exposition of that topic, and I think somewhat easier to understand than the rest of the book. The most precious thing about this book is that the author manages to provide several comprehensive frameworks for enumerativs large classes of enumeration problems. Combinatorics seems a hodge-podge subject to many mathematicians, but Stanley manages to see it as a unified subject with a number of general theories and common techniques.

This book is truly the only text I have ever read that has this perspective on the subject.

I would recommend this book only to someone who has a strong background in mathematics and wants a challenging text that can take them to a deeper level of understanding. Students of combinatorics may want to take this book out of the library and read the introductory pages; there are some particularly useful comments right at the beginning. As a final note, the exercises in this book are also helpful and of diverse difficulty levels–and Stanley classifies the exercises by their difficulty level.

People who find this book difficult to follow may want still benefit from some of the easier exercises. Students wanting an easier-to-follow text might want to check out Cameron’s “Combinatorics”, or Wilf’s “Generatingfunctionology”. As a final note I would like to remark that this book is very reasonably priced, especially when you consider the wealth of material it contains.


Good condition, great book. One person found this helpful. Awesome book to read for a math major! Kindle Edition Verified Purchase. So far so good: It’s a good book, but I haven’t done much surveying of texts in this subject. I am what one of the reviewers called an arm-chair mathematician. While I do not believe, that this book is suitable as a first introduction to combinatorics, it is a great book for anyone, who is interested in the subject and has had some prior exposure.

The formal mathematical prerequisites are quite minimal.

The proofs are such, that after some thinking one can understand them – and they are always rigorous. If one some occasions, the author would have given a short hint, instead of simply saying “it is easily seen” this would have made the book even more readable but even then, after enough thinking one does see, albeit maybe not easily All in all, very recommendable I am referring to volume 1 only, I did not read volume 2 I have now March also read volume II Once again, the formal prerequisites are not very high, but the proofs are definitely harder to understand than in volume I!

A few additional lines of explanation would have made the proofs easier to understand – at least for an “ar chair mathematician”! The book contains mainy excercises with solutions!!! The book is virtually free of any typos, I counted maybe 10 harmless ones. I would still recommend volume II to anybody seriously interested in combinatorics, but it is definitely harder than volume I Overall, my rating remains at “full score”!

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