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

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.

"About this title" may belong to another edition of this title.

Store Description

Visit Seller's Storefront

Seller's business information

BennettBooksLtd
NV, U.S.A.

Sale & Shipping Terms

Terms of Sale

We guarantee the condition of every book as it's described on the Abebooks web sites. If you're dissatisfied with your purchase (Incorrect Book/Not as Described/Damaged) or if the order hasn't arrived, you're eligible for a refund within 30 days of the estimated delivery date. If you've changed your mind about a book that you've ordered, please use the Ask bookseller a question link to contact us and we'll respond within 2 business days.

Shipping Terms

Orders ship within 2 business days. Shipping costs are based on books weighing 2.2 LB, or 1 KG. If your book order is heavy or oversized, we may contact you to let you know extra shipping is required.

Shipping rates within U.S.A.

Shipping rates within U.S.A.
Order quantity	7 to 30 business days	3 to 14 business days
First item	US$ 6.95	US$ 9.95

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.