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 1996-97 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.

Oriented matroids are a very natural mathematical concept which presents itself in many different guises and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the second edition of the first comprehensive, accessible account of the subject. It is intended for a diverse audience: graduate students who wish to learn the subject from scratch; researchers in the various fields of application who want to concentrate on certain aspects of the theory; specialists who need a thorough reference work; and others at academic points in between. A list of exercises and open problems ends each chapter. For the second edition, the authors have expanded the bibliography greatly to ensure that it remains comprehensive and up-to-date, and they have also added an appendix surveying research since the work was first published.