Combinatorics and Commutative Algebra / Edition 2

by Richard P. Stanley

Overview

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 shastic 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.

Product Details

ISBN-13:	9780817643690
Publisher:	Birkh�user Boston
Publication date:	10/15/2004
Series:	Progress in Mathematics , #41
Edition description:	2nd ed. 1996
Pages:	166
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Background.- Nonnegative Integral Solutions to Linear Equations.- The Face Ring of a Simplicial Complex.- Further Aspects of Face Rings.

Editorial Reviews

Provides an overview of connections between commutative algebra and combinatorics. Topics include linear equations in nonnegative integers; integer stochastic matrices; the volume of polytopes; combinatorial reciprocity theorems; and the face ring of a simplicial complex. Features problems and an introductory chapter on algebra, combinatorics, and topology. This second edition contains a chapter surveying recent work in face rings and simplicial complexes, and an application to spline theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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