Combinatorics and Commutative Algebra Paperback - 2004
by Richard P. Stanley
- New
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Details
- Title Combinatorics and Commutative Algebra
- Author Richard P. Stanley
- Binding Paperback
- Edition 2nd
- Condition New
- Pages 166
- Volumes 1
- Language ENG
- Publisher Birkhauser
- Date 2004-10-15
- Features Bibliography
- Bookseller's Inventory # ria9780817643690_pod
- ISBN 9780817643690 / 0817643699
- Weight 0.57 lbs (0.26 kg)
- Dimensions 9.21 x 6.14 x 0.38 in (23.39 x 15.60 x 0.97 cm)
- Dewey Decimal Code 512.24
From the publisher
First line
From the rear 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.