Combinatorics and Commutative Algebra (Progress in Mathematics (Birkhauser Boston)) (Hardcover)

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Key Phrases: upper bound conjecture, simplicial poset, relative simplicial complex, Further Aspects of Face Rings, Nonnegative Integral Solutions, Linear Equations (more...)

Editorial Reviews

Product Description

This text offers an overview of two of the main topics in the connections between commutative algebra and combinatorics. The first concerns the solutions of linear equations in non-negative 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 toplogy aims to broaden access to this material for non-specialists. This edition contains a chapter surveying more recent work related to face rings, focusing on applications to f-vectors. Also included is information on subcomplexes and subdivisions of simplicial complexes, and an application to spline theory.

Product Details

• Hardcover: 164 pages
• Publisher: Birkhauser Verlag; 2 Sub edition (February 1996)
• Language: English
• ISBN-10: 0817638369
• ISBN-13: 978-0817638368
• Product Dimensions: 9.6 x 6.4 x 0.7 inches
• Shipping Weight: 15.8 ounces
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #826,467 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

4.0 out of 5 stars great book, February 12, 2006

By	N. Davison - See all my reviews (REAL NAME)

This review is from: Combinatorics and Commutative Algebra (Progress in Mathematics) (Paperback)

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!

4 of 4 people found the following review helpful:

4.0 out of 5 stars This is a research monograph!, April 19, 2005

By	Loopspace (Norway) - See all my reviews

This review is from: Combinatorics and Commutative Algebra (Progress in Mathematics) (Paperback)

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.