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Combinatorics and Commutative Algebra

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ISBN-10: 0817643699

ISBN-13: 9780817643690

Edition: 2nd 1996 (Revised)

Authors: Massachusetts Institute of Technology Staff, Richard P. Stanley

List price: $79.99
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Description:

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…    
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Book details

List price: $79.99
Edition: 2nd
Copyright year: 1996
Publisher: Birkh�user Boston
Publication date: 10/15/2004
Binding: Paperback
Pages: 166
Size: 6.10" wide x 9.25" long x 0.50" tall
Weight: 1.276
Language: English

Richard P. Stanley is a Professor of Applied Mathematics at the Massachusetts Institute of Technology. He is universally recognized as a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines. He won the AMS 2001 Leroy P. Steele Prize for Mathematical Exposition for his books Enumerative Combinatorics, Volumes 1 and 2, which contain material that form the basis for much of the present book.

Contents
Preface to the Second Edition
Preface to the First Edition
Notation
Background: Combinatorics
Commutative algebra and homological algebra
Topology
Nonnegative Integral Solutions to Linear Equations: Integer stochastic matrices (magic squares)
Graded algebras and modules
Elementary aspects of N-solutions to linear equations
Integer stochastic matrices again
Dimension, depth, and Cohen-Macaulay modules
Local cohomology
Local cohomology of the modules M phi,alpha
Reciprocity
Reciprocity for integer stochastic matrices
Rational points in integer polytopes
Free resolutions
Duality and canonical modules
A final look at linear equations
Gorenstein Hilbert Functions
Further Aspects of
Shellable simplicial
Relative simplical complexes
Index