**Contemporary Mathematics**

Volume: 254;
2000;
432 pp;
Softcover

MSC: Primary 05; 11; 20; 22; 30; 33; 41; 42; 43; 82;

Print ISBN: 978-0-8218-1150-4

Product Code: CONM/254

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

**Electronic ISBN: 978-0-8218-7844-6
Product Code: CONM/254.E**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

# \(q\)-Series from a Contemporary Perspective

Share this page *Edited by *
*Mourad E. H. Ismail; Dennis W. Stanton*

This volume presents the proceedings of the Joint Summer Research Conference on \(q\)-series, combinatorics, and computer algebra held at Mount Holyoke College (South Hadley, MA). All of the papers were contributed by participants and offer original research on topics of current interest. Articles in the book reflect the diversity of areas that overlap with \(q\)-series, as well as the usefulness of \(q\)-series across the mathematical sciences. The conference was held in honor of Richard Askey on the occasion of his 65th birthday and the proceedings contain an article about Askey's contributions to special functions.

#### Readership

Graduate students and research mathematicians interested in combinatorics.

# Table of Contents

## $q$-Series from a Contemporary Perspective

- Contents vii8 free
- Preface ix10 free
- The mathematical contributions of Richard Askey 112 free
- Curriculum vitae of Richard A. Askey 1930
- Reformulations of a partition theorem of Göllnitz and q-series identities 3142
- Schur's theorem, partitions with odd parts and the Al-Salam-Carlitz polynomials 4556
- Singularity and monodromy of quasi-hypergeometric functions 5768
- Incomplete elliptic integrals in Ramanujan's lost notebook 7990
- Measure algebras associated with orthogonal polynomials 127138
- Word straightening and q-Eulerian calculus 141152
- Path generating transforms 157168
- q-extensions of Erdélyi's fractional integral representations for hypergeometric functions and some summation formulas for double q-Kampé de Fériet series 187198
- Numerical investigation of basic Fourier series 199210
- An identity of Ramanujan, and applications 229240
- Addition theorems for the q-exponential function 235246
- The Schur functions for partitions with complex parts 247258
- On Forrester's generalization of Morris constant term identity 271282
- New combinatorial formula for modified Hall-Littlewood polynomials 283294
- §0. Introduction 285296
- §1. Modified Hall-Littlewood polynomials 288299
- 1.1. Definition 288299
- 1.2. Modified Hall–Littlewood polynomials for partition λ = (1N) 289300
- 1.3. Hall-Littlewood polynomials and characters of the affine Lie algebra sl(n) 290301
- 1.4. Modified Hall-Littlewood polynomials and unipotent flag varieties 291302
- 1.5. Modified Hall–Littlewood polynomials and Demazure characters 291302
- 1.6. Modified Hall–Littlewood polynomials and chains of subgroupsin a finite abelian p–group 292303

- §2. Generalized mahonian statistics 296307
- §3. Main results 302313
- §4. Proofs of Theorems 3.1 and 3.4 309320
- §5. Polynomials Pλμ(t) and their interpretations 313324
- §6. Generalizations of polynomials Pλμ(t) and Kλμ(t) 316327
- §7. Fermionic formulae 324335
- §8. Two parameter deformation of one dimensional sums 329340
- References 331342

- Schur function identities and the number of perfect matchings of Holey Aztec rectangles 335346
- A new U(n) generalization of the Jacobi triple product identity 351362
- A new quantum algebraic interpretation of the Askey-Wilson polynomials 371382
- Some properties of Koornwinder polynomials 395406
- A new multidimensional matrix inversion in Ar 413424