Progress in Mathematics

Combinatorics and Commutative Algebra

Authors: Stanley, Richard

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About this Textbook

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.

Table of contents (4 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-4433-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.95
price for USA
  • ISBN 978-0-8176-4369-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorics and Commutative Algebra
Authors
Series Title
Progress in Mathematics
Series Volume
41
Copyright
1996
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4433-8
DOI
10.1007/b139094
Softcover ISBN
978-0-8176-4369-0
Series ISSN
0743-1643
Edition Number
2
Number of Pages
XII, 168
Topics