Combinatorics and Commutative Algebra

Stanley, Richard P.

ISBN 10: 0817643699 / ISBN 13: 9780817643690

Published by Birkhauser Boston Inc, 2004

About this Item

Contains a significant amount of new in areas of interest, and presents the "big picture" in an engaging framework. Series: Progress in Mathematics. Num Pages: 168 pages, biography. BIC Classification: PBF. Category: (UU) Undergraduate. Dimension: 234 x 156 x 9. Weight in Grams: 580. . 2004. 2nd. Paperback. . . . .

Seller Inventory # V9780817643690

Bibliographic Details

• Title: Combinatorics and Commutative Algebra
• Publisher: Birkhauser Boston Inc
• Publication Date: 2004
• Language: English
• ISBN 10: 0817643699
• ISBN 13: 9780817643690
• Binding: Soft cover
• Edition: 2nd Edition
• Condition: New

About this title

Synopsis

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.

From the Back Cover

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. Included in this chapter is an outline of the proof of McMullen's g-conjecture for simplicial polytopes based on toric varieties, as well as a discussion of the face rings of such special classes of simplicial complexes as shellable complexes, matroid complexes, level complexes, doubly Cohen-Macaulay complexes, balanced complexes, order complexes, flag complexes, relative complexes, and complexes with group actions. Also included is information on subcomplexes and subdivisions of simplicial complexes, and an application to spline theory.