New Perspectives in Algebraic Combinatorics (Mathematical Sciences Research Institute Publications) [Hardcover]

Louis J. Billera (Editor), Anders Björner (Editor), Curtis Greene (Editor), Rodica E. Simion (Editor), Richard P. Stanley (Editor)

Book Description

ISBN-10: 0521770874 | ISBN-13: 978-0521770873 | Publication Date: September 28, 1999 0

During 1996-97 MSRI held a full academic-year program on combinatorics, with special emphasis on its connections to other branches of mathematics, such as algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. The rich combinatorial problems arising from the study of various algebraic structures are the subject of this book, which features work done or presented at the program's seminars. The text contains contributions on matroid bundles, combinatorial representation theory, lattice points in polyhedra, bilinear forms, combinatorial differential topology and geometry, Macdonald polynomials and geometry, enumeration of matchings, the generalized Baues problem, and Littlewood-Richardson semigroups. These expository articles, written by some of the most respected researchers in the field, present the state of the art to graduate students and researchers in combinatorics as well as in algebra, geometry, and topology.

Editorial Reviews

Book Description

During 1996-97 MSRI held a full academic year program on Combinatorics, with special emphasis on the connections with other branches of mathematics, such as algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. The rich combinatorial problems arising from the study of various algebraic structures are the subject of this book, which contains expository contributions by some of the most respected researchers in the field. It will present the state of the art to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.

Product Details

• Hardcover: 355 pages
• Publisher: Cambridge University Press (September 28, 1999)
• Language: English
• ISBN-10: 0521770874
• ISBN-13: 978-0521770873
• Product Dimensions: 9.3 x 6.2 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,416,961 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

5.0 out of 5 stars A wonderful collection of research-expository surveys, August 22, 2000

By 

Timothy Chow - See all my reviews
(REAL NAME)   

This review is from: New Perspectives in Algebraic Combinatorics (Mathematical Sciences Research Institute Publications) (Hardcover)

This volume contains expository introductions to some of the most exciting research areas in algebraic combinatorics. Although most of the articles began life as a lecture at MSRI, the authors have done much more than publish transcripts of their talks; they have produced carefully written articles that contain much information that they could not present during the severe time constraints of the original combinatorics seminar. Anyone interested in entering one of the fields touched upon in this volume would be hard-pressed to find a better way to get started than to study the relevant article in this book.

Since the articles were written there have of course been advances; I will just mention that a number of Jim Propp's matchings problems have been solved, and that Mark Haiman has proved the n! conjecture.

Contents: Matroid bundles (L. Anderson); Combinatorial representation theory (H. Barcelo, A. Ram); An algorithmic theory of lattice points in polyhedra (A. Barvinok, J. E. Pommersheim); Some algebraic properties of the Schechtman-Varchenko bilinear forms (G. Denham, P. Hanlon); Combinatorial differential topology and geometry (R. Forman); Macdonald polynomials and geometry (M. Haiman); Enumeration of matchings: problems and progress (J. Propp); The generalized Baues problem (V. Reiner); Littlewoord-Richardson semigroups (A. Zelevinsky).