During 1996-97, the Mathematical Sciences Research Institute held a full academic year program on combinatorics, with special emphasis on the connectoins 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, present the state of the art to researchers and graduate students in combinatorics as well as algebra, geometry, and topology.
- Matroid Bundles
- Combinatorial Representation Theory
- An Algorithmic Theory of Lattice Points in Polyhedra
- Some Algebraic Properties of the Schechtman-Varchenko Bilinear Forms
- Combinatorial Differential Topology and Geometry
- Macdonald Polynomials and Geometry
- Enumeration of Matchings: Problems and Progress
- The Generalized Baues Problem
- Littlewood - Richardson Semigroups