Q-Series and Partitions

ISBN-13: 9781468406399 / Angielski / Miękka / 2012 / 212 str.

Dennis Stanton

Opis

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."

Spis treści

On the Proofs of the Rogers-Ramanujan Identities.- Bibasic Summation, Transformation and Expansion Formulas, q-Analogues of Clausen’s Formula, and Nonnegative Basic Hypergeometric Series.- Identities.- In the Land of Oz.- On the Gaussian Polynomials.- A One-line High School Algebra Proof of the Unimodality of the Gaussian Polynomials [nk] for k < 20.- An Elementary Proof of a q-Binomial Identity.- Some Macdonald-Mehta Integrals by Brute Force.- Macdonald Conjectures and the Selberg Integral.- Analogs and Extensions of Selberg’s Integral.- An Elementary Approach to the Macdonald Identities.- Continuous q-Hermite Polynomials when q > 1.- Generalized Rook Polynomials and Orthogonal Polynomials.- Monotonicity of Zeros of Orthogonal Polynomials.- Symmetry Techniques and Orthogonality for q-Series.