New Perspectives in Algebraic Combinatorics

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.

During 1996–7 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 Littlewood–Richardson semigroups. These expository articles, written by some of the most respected researchers in the field, will continue to be of use to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.

Preface; 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.

This 2000 book contains expository contributions by respected researchers on the rich combinatorial problems arising from the study of algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. It will continue to be of use to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.