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George E. Andrews 80 Years of Combinatory Analysis

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  • © 2021

Overview

Editors:
  1. Krishnaswami Alladi

    1. Department of Mathematics, University of Florida, Gainesville, USA

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  2. Bruce C. Berndt

    1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

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  3. Peter Paule

    1. Research Institute for Symbolic Computation, Johannes Kepler University Linz, Linz, Austria

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  4. James A. Sellers

    1. Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, USA

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  5. Ae Ja Yee

    1. Department of Mathematics, Pennsylvania State University, University Park, USA

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  • Contains many private and work related photographs
  • Dedicated to George Andrews’ 80th Birthday
  • Complemented by special personal contributions

Part of the book series: Trends in Mathematics (TM)

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Table of contents (43 chapters)

  1. Front Matter

    Pages i-ix
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  2. Personal Contributions

    1. Front Matter

      Pages 1-1
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    2. The Worlds of George Andrews, a Daughter’s Take

      • Amy Alznauer
      Pages 3-7

    3. My Association and Collaboration with George Andrews

      • Krishnaswami Alladi
      Pages 9-31

    4. Ramanujan, His Lost Notebook, Its Importance

      • Bruce C. Berndt
      Pages 33-52

  3. Photographs

    1. Front Matter

      Pages 53-53
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    2. George Andrews: “Combinatory Analysis 80” Picture Book

      • Peter Paule
      Pages 55-70

  4. Articles

    1. Front Matter

      Pages 71-71
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    2. Dissections of Strange q-Series

      • Scott Ahlgren, Byungchan Kim, Jeremy Lovejoy
      Pages 73-88

    3. Dyson’s “Favorite” Identity and Chebyshev Polynomials of the Third and Fourth Kind

      • George E. Andrews
      Pages 89-110

    4. A q-Translation Approach to Liu’s Calculus

      • Hatice Aslan, Mourad E. H. Ismail
      Pages 111-134

    5. Combinations of Ranks and Cranks of Partitions Moduli 6, 9 and 12 and Their Comparison with the Partition Function

      • Zafer Selcuk Aygin, Song Heng Chan
      Pages 135-155

    6. Combinatorial Proofs of Two Euler-Type Identities Due to Andrews

      • Cristina Ballantine, Richard Bielak
      Pages 157-171

    7. Noncommutative Catalan Numbers

      • Arkady Berenstein, Vladimir Retakh
      Pages 173-193

    8. Elementary Polynomial Identities Involving q-Trinomial Coefficients

      • Alexander Berkovich, Ali Kemal Uncu
      Pages 195-206

    9. A Partial Theta Function Borwein Conjecture

      • Gaurav Bhatnagar, Michael J. Schlosser
      Pages 207-218

    10. A Note on Andrews’ Partitions with Parts Separated by Parity

      • Kathrin Bringmann, Chris Jennings-Shaffer
      Pages 219-224

    11. A Bijective Proof of a False Theta Function Identity from Ramanujan’s Lost Notebook

      • Hannah E. Burson
      Pages 225-234

    12. Quasipolynomials and Maximal Coefficients of Gaussian Polynomials

      • Angelica Castillo, Stephanie Flores, Anabel Hernandez, Brandt Kronholm, Acadia Larsen, Arturo Martinez
      Pages 235-257

    13. Finding Modular Functions for Ramanujan-Type Identities

      • William Y. C. Chen, Julia Q. D. Du, Jack C. D. Zhao
      Pages 259-303
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Keywords

About this book

This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018.
This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics.
In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area.

The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt.
Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection.
In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”.

This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.





Editors and Affiliations

  • Department of Mathematics, University of Florida, Gainesville, USA

    Krishnaswami Alladi

  • Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

    Bruce C. Berndt

  • Research Institute for Symbolic Computation, Johannes Kepler University Linz, Linz, Austria

    Peter Paule

  • Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, USA

    James A. Sellers

  • Department of Mathematics, Pennsylvania State University, University Park, USA

    Ae Ja Yee

Bibliographic Information

  • Book Title: George E. Andrews 80 Years of Combinatory Analysis

  • Editors: Krishnaswami Alladi, Bruce C. Berndt, Peter Paule, James A. Sellers, Ae Ja Yee

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-57050-7

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-57049-1Published: 11 February 2021

  • Softcover ISBN: 978-3-030-57052-1Published: 11 February 2022

  • eBook ISBN: 978-3-030-57050-7Published: 10 February 2021

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: IX, 810

  • Number of Illustrations: 3 b/w illustrations, 37 illustrations in colour

  • Topics: Number Theory, Special Functions, Combinatorics

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