Combinatorial and Additive Number Theory III

1. Front Matter

   Pages i-viii

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2. Weighted Zero-Sums for Some Finite Abelian Groups of Higher Ranks

   • S. D. Adhikari, Bidisha Roy, Subha Sarkar

   Pages 1-12

3. Counting Monogenic Cubic Orders

   • Shabnam Akhtari

   Pages 13-24

4. The Zeckendorf Game

   • Paul Baird-Smith, Alyssa Epstein, Kristen Flint, Steven J. Miller

   Pages 25-38

5. Iterated Riesel and Iterated Sierpiński Numbers

   • Holly Paige Chaos, Carrie E. Finch-Smith

   Pages 39-54

6. A General Framework for Studying Finite Rainbow Configurations

   • Mike Desgrottes, Steven Senger, David Soukup, Renjun Zhu

   Pages 55-63

7. Translation Invariant Filters and van der Waerden’s Theorem

   • Mauro Di Nasso

   Pages 65-74

8. Central Values for Clebsch–Gordan Coefficients

   • Robert W. Donley Jr.

   Pages 75-100

9. Numerical Semigroups Generated by Squares and Cubes of Three Consecutive Integers

   • Leonid G. Fel

   Pages 101-121

10. On Supra-SIM Sets of Natural Numbers

    • Isaac Goldbring, Steven Leth

    Pages 123-132

11. Mean Row Values in (u, v)-Calkin–Wilf Trees

    • Sandie Han, Ariane M. Masuda, Satyanand Singh, Johann Thiel

    Pages 133-146

12. Dimensions of Monomial Varieties

    • Melvyn B. Nathanson

    Pages 147-160

13. Matrix Scaling Limits in Finitely Many Iterations

    • Melvyn B. Nathanson

    Pages 161-167

14. Not All Groups Are LEF Groups, or Can You Know If a Group Is Infinite?

    • Melvyn B. Nathanson

    Pages 169-174

15. Binary Quadratic Forms in Difference Sets

    • Alex Rice

    Pages 175-196

16. Egyptian Fractions, Nonstandard Extensions of \(\mathbb R\), and Some Diophantine Equations Without Many Solutions

    • David A. Ross

    Pages 197-207

17. A Dual-Radix Approach to Steiner’s 1-Cycle Theorem

    • Andrey Rukhin

    Pages 209-226

18. Potentially Stably Rational Del Pezzo Surfaces over Nonclosed Fields

    • Yuri Tschinkel, Kaiqi Yang

    Pages 227-233

Based on talks from the 2017 and 2018 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 17 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. Topics featured in this volume include sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, commutative algebra and discrete geometry, and applications of logic and nonstandard analysis to number theory. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory. 

• additive number theory
• combinatorial number theory
• Goldbach conjecture
• computer science
• Newman conjecture
• Selberg class of L-functions
• combinatorics
• cryptography

• Department of Mathematics, Lehman College and the Graduate Center, City University of New York, New York, USA

  Melvyn B. Nathanson

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

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