E-Book Overview
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.
E-Book Content
New Perspectives in Geometric Combinatorics MSRI Publications Volume 38, 1999
Contents
Preface
ix
Matroid Bundles Laura Anderson
1
Combinatorial Representation Theory H´ el` ene Barcelo and Arun Ram
23
An Algorithmic Theory of Lattice Points in Polyhedra Alexander Barvinok and James E. Pommersheim
91
Some Algebraic Properties of the Schechtman–Varchenko Bilinear Forms Graham Denham and Phil Hanlon
149
Combinatorial Differential Topology and Geometry Robin Forman
177
Macdonald Polynomials and Geometry Mark Haiman
207
Enumeration of Matchings: Problems and Progress James Propp
255
The Generalized Baues Problem Victor Reiner
293
Littlewood–Richardson Semigroups Andrei Zelevinsky
337
vii
New Perspectives in Geo