New Perspectives in Algebraic Combinatorics

Rating:
Summary: A wonderful collection of research-expository surveys
Review: This volume contains expository introductions to some of the most exciting research areas in algebraic combinatorics. Although most of the articles began life as a lecture at MSRI, the authors have done much more than publish transcripts of their talks; they have produced carefully written articles that contain much information that they could not present during the severe time constraints of the original combinatorics seminar. Anyone interested in entering one of the fields touched upon in this volume would be hard-pressed to find a better way to get started than to study the relevant article in this book.

Since the articles were written there have of course been advances; I will just mention that a number of Jim Propp's matchings problems have been solved, and that Mark Haiman has proved the n! conjecture.

Contents: Matroid bundles (L. Anderson); Combinatorial representation theory (H. Barcelo, A. Ram); An algorithmic theory of lattice points in polyhedra (A. Barvinok, J. E. Pommersheim); Some algebraic properties of the Schechtman-Varchenko bilinear forms (G. Denham, P. Hanlon); Combinatorial differential topology and geometry (R. Forman); Macdonald polynomials and geometry (M. Haiman); Enumeration of matchings: problems and progress (J. Propp); The generalized Baues problem (V. Reiner); Littlewoord-Richardson semigroups (A. Zelevinsky).

Rating:
Summary: A wonderful collection of research-expository surveys
Review: This volume contains expository introductions to some of the most exciting research areas in algebraic combinatorics. Although most of the articles began life as a lecture at MSRI, the authors have done much more than publish transcripts of their talks; they have produced carefully written articles that contain much information that they could not present during the severe time constraints of the original combinatorics seminar. Anyone interested in entering one of the fields touched upon in this volume would be hard-pressed to find a better way to get started than to study the relevant article in this book.

Since the articles were written there have of course been advances; I will just mention that a number of Jim Propp's matchings problems have been solved, and that Mark Haiman has proved the n! conjecture.

Contents: Matroid bundles (L. Anderson); Combinatorial representation theory (H. Barcelo, A. Ram); An algorithmic theory of lattice points in polyhedra (A. Barvinok, J. E. Pommersheim); Some algebraic properties of the Schechtman-Varchenko bilinear forms (G. Denham, P. Hanlon); Combinatorial differential topology and geometry (R. Forman); Macdonald polynomials and geometry (M. Haiman); Enumeration of matchings: problems and progress (J. Propp); The generalized Baues problem (V. Reiner); Littlewoord-Richardson semigroups (A. Zelevinsky).