Synopses & Reviews
Expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.
Synopsis
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.
Table of Contents
1. Matroid bundles Laura Anderson; 2. Combinatorial representation theory Helene Barcelo and Arun Ram; 3. An algorithmic theory of lattice points in polyhedra Alexander Barvinok and James Pommersheim; 4. Some algebraic properties of the Schechtman-Varchenko bilinear forms Graham Denham and Phil Hanlon; 5. Combinatorial differential topology and geometry Robin Forman; 6. Macdonald polynomials and geometry Mark Haiman; 7. Enumeration of matchings: problems and progress James Propp; 8. The generalized Baues problem Victor Reiner; 9. Littlewood-Richardson semigroups Andrei Zelevinsky.