New perspectives in algebraic combinatorics

Louis J. Billera, Anders Björner, Curtis Greene, Rodica E. Simion, Richard P. Stanley0521770874, 9780521770873

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.

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Table of contents :
Table of Contents……Page 1
Preface……Page 3
Matroid Bundles……Page 4
Combinatorial Representation Theory……Page 26
An Algorithmic Theory of Lattice Pointsin Polyhedra……Page 95
Some Algebraic Properties of theSchechtman{Varchenko Bilinear Forms……Page 153
Combinatorial Differential Topology and Geometry……Page 181
Macdonald Polynomials and Geometry……Page 211
Enumeration of Matchings – Problems and Progress……Page 259
The Generalized Baues Problem……Page 297
Littlewood–Richardson Semigroups……Page 341