New Perspectives in Algebraic Combinatorics

by Edited by Louis J. Billera , Anders Björner , Curtis Greene , Rodica E. Simion , Richard P. Stanley

• ISBN13: 9780521770873
• ISBN10: 0521770874
• Format: Hardcover
• Copyright: 1999-09-28
• Publisher: Cambridge University Press

Summary

During 199697 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 represents work done or presented at seminars during the program. It 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 LittlewoodRichardson semigroups. These expository articles, written by some of the most respected researchers in the field, will present the state of the art to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.

Table of Contents

Preface	ix
Matroid Bundles	1	(22)
Laura Anderson
Combinatorial Representation Theory	23	(68)
Helene Barcelo
Arun Ram
An Algorithmic Theory of Lattice Points in Polyhedra	91	(58)
Alexander Barvinok
James E. Pommersheim
Some Algebraic Properties of the Schechtman--Varchenko Bilinear Forms	149	(28)
Graham Denham
Phil Hanlon
Combinatorial Differential Topology and Geometry	177	(30)
Robin Forman
Macdonald Polynomials and Geometry	207	(48)
Mark Haiman
Enumeration of Matchings: Problems and Progress	255	(38)
James Propp
The Generalized Baues Problem	293	(44)
Victor Reiner
Littlewood--Richardson Semigroups	337
Andrei Zelevinsky