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Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra

In Honour of Peter Paule on his 60th Birthday

  • Book
  • © 2020

Overview

Editors:
  1. Veronika Pillwein

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

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    You can also search for this editor in PubMed   Google Scholar

  2. Carsten Schneider

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

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Up-to-date reviews on hot topics in mathematics
  • Interdisciplinary research between highly visible research areas
  • Focuses on algorithmic aspects
  • Surveys existing software packages relating to the topics

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. When the Search for Solutions Can Be Terminated

    • Sergei A. Abramov
    Pages 1-7

  3. Euler’s Partition Theorem and Refinements Without Appeal to Infinite Products

    • Krishnaswami Alladi
    Pages 9-23

  4. Sequences in Partitions, Double q-Series and the Mock Theta Function ρ3(q)

    • George E. Andrews
    Pages 25-45

  5. Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities

    • Alexander Berkovich, Ali Kemal Uncu
    Pages 47-61

  6. Large Scale Analytic Calculations in Quantum Field Theories

    • Johannes Blümlein
    Pages 63-87

  7. An Eigenvalue Problem for the Associated Askey–Wilson Polynomials

    • Andrea Bruder, Christian Krattenthaler, Sergei K. Suslov
    Pages 89-108

  8. Context-Free Grammars and Stable Multivariate Polynomials over Stirling Permutations

    • William Y. C. Chen, Robert X. J. Hao, Harold R. L. Yang
    Pages 109-135

  9. An Interesting Class of Hankel Determinants

    • Johann Cigler, Mike Tyson
    Pages 137-157

  10. A Sequence of Polynomials Generated by a Kapteyn Series of the Second Kind

    • Diego Dominici, Veronika Pillwein
    Pages 159-179

  11. Comparative Analysis of Random Generators

    • Johannes vom Dorp, Joachim von zur Gathen, Daniel Loebenberger, Jan Lühr, Simon Schneider
    Pages 181-196

  12. Difference Equation Theory Meets Mathematical Finance

    • Stefan Gerhold, Arpad Pinter
    Pages 197-213

  13. Evaluations as L-Subsets

    • Adalbert Kerber
    Pages 215-222

  14. Exact Lower Bounds for Monochromatic Schur Triples and Generalizations

    • Christoph Koutschan, Elaine Wong
    Pages 223-248

  15. Evaluation of Binomial Double Sums Involving Absolute Values

    • Christian Krattenthaler, Carsten Schneider
    Pages 249-295

  16. On Two Subclasses of Motzkin Paths and Their Relation to Ternary Trees

    • Helmut Prodinger, Sarah J. Selkirk, Stephan Wagner
    Pages 297-316

  17. A Theorem to Reduce Certain Modular Form Relations Modulo Primes

    • Cristian-Silviu Radu
    Pages 317-337

  18. Trying to Solve a Linear System for Strict Partitions in ‘Closed Form’

    • Volker Strehl
    Pages 339-386

  19. Untying the Gordian Knot via Experimental Mathematics

    • Yukun Yao, Doron Zeilberger
    Pages 387-410
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Keywords

About this book

The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.

Editors and Affiliations

  • Research Institut for Symbolic Computation, Johannes Kepler University of Linz, Linz, Austria

    Veronika Pillwein, Carsten Schneider

Bibliographic Information

  • Book Title: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra

  • Book Subtitle: In Honour of Peter Paule on his 60th Birthday

  • Editors: Veronika Pillwein, Carsten Schneider

  • Series Title: Texts & Monographs in Symbolic Computation

  • DOI: https://doi.org/10.1007/978-3-030-44559-1

  • Publisher: Springer Cham

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-44558-4Published: 29 September 2020

  • Softcover ISBN: 978-3-030-44561-4Published: 30 September 2021

  • eBook ISBN: 978-3-030-44559-1Published: 28 September 2020

  • Series ISSN: 0943-853X

  • Series E-ISSN: 2197-8409

  • Edition Number: 1

  • Number of Pages: XVII, 410

  • Number of Illustrations: 36 b/w illustrations, 19 illustrations in colour

  • Topics: Symbolic and Algebraic Manipulation, Mathematical Applications in Computer Science

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