During 1996-97 MSRI held a full academic year program on Combinatorics, with special emphasis on algebraic combinatorics and its connections with other branches of mathematics, such as algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. Different periods of the year were devoted to research in enumeration, extremal questions, geometric combinatorics and representation theory.
The rich combinatorial problems arising from the study of these
various
areas 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 graduate
students and researchers in combinatorics as well as algebra,
geometry,
and topology.