Combinatorics and Commutative Algebra
By addebook • Jul 14th, 2008 • Category: Mathematics •
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Combinatorics and Commutative Algebra (Progress in Mathematics)
Combinatorics and Commutative Algebra (Progress in Mathematics)
By Richard P. Stanley
Publisher: Birkhäuser Boston
Number Of Pages: 180
Publication Date: 2004-10-15
ISBN-10 / ASIN: 0817643699
ISBN-13 / EAN: 9780817643690
Binding: Paperback
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists.
New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors.
Summary: great book
Rating: 4
Great book - just be ready to get hold of some other books to fill in the details. If you’re not entirely comfortable with the stuff in chapter 0 concerning modules (projectivity, injectivity), tor and ext, and homology from topology, maybe find a quick introduction to these elsewhere - while its certainly possible to learn about these things from chapter 0 of this book, it’s not exactly the most painless way to do it. It was my first book on the subject, then I got Miller and Sturmfels: it would make more sense to reverse that order. Better still, get both simultaneously, and when the Stanley becomes a bit dense refer to M S. I really loved this book, but it was damn hard at times!
Summary: This is a research monograph!
Rating: 4
For those looking for a thorough introduction to the theory in this book, I would suggest a look at Miller and Sturmfels recent book on combinatorial commutative algebra or the book on Cohen-Macaulay rings by Bruns and Herzog. This is a great book, but I don’t think it was intended as a beginners first book . Instead its style concentrates on presenting results found in research-articles ( prior to this book, there doesn’t seem to have been any texts giving an overview of the theory ). It is great for looking up results, reading the needed prerequisites without going into details and finding important references.
Summary: I dont read this book yet!
Rating: 1
I dont read this book yet!
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