q-Series and Partitions

Overview

This volume contains the proceedings of the workshop held for the Applied Combinatorics program in March, 1988. The central idea of the workshop is the recent interplay of the classical analysis of q-series, and the combinatorial analysis of partitions of intergers. Many related topics are discussed, including orthogonal polynomials, the Macdonald conjectures for root systems, and related integrals. Those people interested in combinatorial enumeration and special functions will find this volume of interest. ...

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Paperback (Softcover reprint of the original 1st ed. 1989)
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Overview

This volume contains the proceedings of the workshop held for the Applied Combinatorics program in March, 1988. The central idea of the workshop is the recent interplay of the classical analysis of q-series, and the combinatorial analysis of partitions of intergers. Many related topics are discussed, including orthogonal polynomials, the Macdonald conjectures for root systems, and related integrals. Those people interested in combinatorial enumeration and special functions will find this volume of interest. Recent applications of q-series (and related functions) to exactly solvable statistical mechanics models and to statistics makes this volume of interest to non-specialists. Included are several expository papers, and a series of papers on new work on the unimodality of the q-binomial coefficient.

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Product Details

  • ISBN-13: 9781468406399
  • Publisher: Springer New York
  • Publication date: 3/2/2012
  • Series: IMA Volumes in Mathematics and its Applications Series , #18
  • Edition description: Softcover reprint of the original 1st ed. 1989
  • Edition number: 1
  • Pages: 212
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.48 (d)

Table of Contents

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.

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