q-Series and Partitions PDF

This IMA Volume in Mathematics and its Applications q-Series and Partitions is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS.

We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year- long program.

We especially thank the Workshop Organizer, Dennis Stanton, for organizing a workshop which brought together many of the major figures in a variety of research fields in which q-series and partitions are used.

A vner Friedman Willard Miller, Jr. PREFACE This volume contains the Proceedings of the Workshop on q-Series and Parti- tions held at the IMA on March 7-11, 1988.

Also included are papers by Goodman and O'Hara, Macdonald, and Zeilberger on unimodality.

This work was of substan- tial interest and discussed by many participants in the Workshop.

The papers have been grouped into four parts: identities, unimodality of Gaus- sian polynomials, constant term problems and related integrals, and orthogonal polynomials.

They represent a cross section of the recent work on q-series includ- ing: partitions, combinatorics, Lie algebras, analysis, and mathematical physics.

I would like to thank the staff of the IMA, and its directors, Avner Friedman and Willard Miller, Jr., for providing a wonderful environment for the Workshop.

Patricia Brick and Kaye Smith prepared the manuscripts.