Combinatorics and Commutative Algebra
Series: Progress in Mathematics; 41;
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Product details:
- Edition number 2
- Publisher Birkhäuser Boston
- Date of Publication 15 October 2004
- Number of Volumes 1 pieces, Book
- ISBN 9780817643690
- Binding Paperback
- No. of pages166 pages
- Size 235x155 mm
- Weight 580 g
- Language English
- Illustrations IX, 166 p. 0
Categories
Long description:
"
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.
The author is well known to the math community as an excellent researcher and expositor in the fields of combinatorics and algebra. His first book was widely read. In this second edition, which contains a significant amount of new material in areas of current interest, Stanley, as before, presents the ""big picture"" in an engaging framework." MoreTable of Contents:
Background.- Nonnegative Integral Solutions to Linear Equations.- The Face Ring of a Simplicial Complex.- Further Aspects of Face Rings.
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