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Combinatorial and Additive Number Theory II

CANT, New York, NY, USA, 2015 and 2016

  • Conference proceedings
  • © 2017

Overview

Editors:
  1. Melvyn B. Nathanson

    1. Department of Mathematics, Lehman College (CUNY), Bronx, USA

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  • Collates recent advances in combinatorial and additive number theory from distinguished mathematicians in the field
  • Points to future areas of research
  • All papers feature original, peer-reviewed content

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 220)

Included in the following conference series:

Conference proceedings info: CANT 2015. CANT 2016.

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Table of contents (20 papers)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. On a Conjecture of Fox and Kleitman on the Degree of Regularity of a Certain Linear Equation

    • Sukumar Das Adhikari, Shalom Eliahou
    Pages 1-8

  3. Open Problems About Sumsets in Finite Abelian Groups: Minimum Sizes and Critical Numbers

    • Béla Bajnok
    Pages 9-23

  4. Benford Behavior of Generalized Zeckendorf Decompositions

    • Andrew Best, Patrick Dynes, Xixi Edelsbrunner, Brian McDonald, Steven J. Miller, Kimsy Tor et al.
    Pages 25-37

  5. Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions

    • Andrew Best, Karen Huan, Nathan McNew, Steven J. Miller, Jasmine Powell, Kimsy Tor et al.
    Pages 39-52

  6. Recurrence Identities of b-ary Partitions

    • Dakota Blair
    Pages 53-83

  7. Cryptographic Hash Functions and Some Applications to Information Security

    • Lisa Bromberg
    Pages 85-97

  8. Numerical Sets, Core Partitions, and Integer Points in Polytopes

    • Hannah Constantin, Ben Houston-Edwards, Nathan Kaplan
    Pages 99-127

  9. Pairs of Dot Products in Finite Fields and Rings

    • David Covert, Steven Senger
    Pages 129-138

  10. Characteristic, Counting, and Representation Functions Characterized

    • Charles Helou
    Pages 139-155

  11. Partitions into Parts Simultaneously Regular, Distinct, And/or Flat

    • William J. Keith
    Pages 157-170

  12. White’s Theorem

    • Mizan R. Khan, Karen M. Rogers
    Pages 171-180

  13. A Misère-Play \(\star \)-Operator

    • Matthieu Dufour, Silvia Heubach, Urban Larsson
    Pages 181-198

  14. A New Proof of Khovanskiĭ’s Theorem on the Geometry of Sumsets

    • Jaewoo Lee
    Pages 199-204

  15. Initial Sums of the Legendre Symbol: Is \(\min + \max \ge 0\) ?

    • Kieren MacMillan, Jonathan Sondow
    Pages 205-213

  16. A Second Wave of Expanders in Finite Fields

    • Brendan Murphy, Giorgis Petridis
    Pages 215-238

  17. Sumsets Contained in Sets of Upper Banach Density 1

    • Melvyn B. Nathanson
    Pages 239-248

  18. The Erdős Paradox

    • Melvyn B. Nathanson
    Pages 249-254

  19. Limits and Decomposition of de Bruijn’s Additive Systems

    • Melvyn B. Nathanson
    Pages 255-267

  20. Extending Babbage’s (Non-)Primality Tests

    • Jonathan Sondow
    Pages 269-277
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  1. Combinatorial and Additive Number Theory II

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About this book

Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling. 

Editors and Affiliations

  • Department of Mathematics, Lehman College (CUNY), Bronx, USA

    Melvyn B. Nathanson

About the editor

Melvyn B. Nathanson is a Professor of Mathematics at the City University of New York.

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