Authors:
- Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra
- The theory of invariants of a torus acting linearly on a polynomial ring
- The face ring of a simplicial complex
- The author develops some interesting properties of face rings with application to combinatorics
Part of the book series: Progress in Mathematics (PM, volume 41)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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Department of Mathematics, Massachusetts Institute of Technology, Cambridge
Richard P. Stanley
Bibliographic Information
Book Title: Combinatorics and Commutative Algebra
Authors: Richard P. Stanley
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/b139094
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Birkhäuser Boston 1996
Softcover ISBN: 978-0-8176-4369-0Published: 15 October 2004
eBook ISBN: 978-0-8176-4433-8Published: 13 December 2007
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 2
Number of Pages: IX, 166
Topics: Combinatorics, Commutative Rings and Algebras, Topology