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.
Preface.-
1. S.D. Adhikari, B. Roy, S. Sarkar: Weighted Zero-Sums for
Some Finite Abelian Groups of Higher Ranks.-
2. S. Akhtari: Counting
Monogenic Cubic Orders.-
3. P. Baird-Smith, A. Epstein, K. Flint, S.J.
Miller: The Zeckendorf Game.-
4. H.P. Chaos, C.E. Finch-Smith: Iterated
Riesel and Iterated Sierpinski Numbers.-
5. M. Desgrottes, S. Senger, D.
Soukup, R. Zhu: A General Framework for Studying Finite Rainbow
Configurations.-
6. M. DiNasso: Translation Invariant Filters and van der
Waerden's Theorem.- 7. R.W. Donley, Jr.: Central Values for Clebsch-Gordan
Coefficients.-
8. L.G. Fel: Numerical Semigroups Generated by Squares and
Cubes of Three Consecutive Integers.-
9. I. Goldbring, S. Leth: On Supra-sim
Sets of Natural Numbers.-
10. S. Han, A.M. Masuda, S. Singh, J. Thiel: Mean
Row Values in (u.v)-Calkin-Wilf Trees.-
11. M.B. Nathanson: Dimensions of
Monomial Varieties.-
12. Matrix Scaling Limits in Finitely Many Iterations
(M.B. Nathanson).-
13. M.B. Nathanson: Not All Groups are LEF Groups, or, Can
You Know if a Group is Infinite?.-
14. A. Rice: Binary Quadratic Forms in
Difference Sets.- 15. D.A. Ross: Egyptian Fractions, Non-Archimedean Ordered
Field, Nonstandard Analysis.-
16. A. Rukhin: A Dual-Radix Approach to
Steiner's 1-Cycle Theorem.-
17. Y. Tschinkel, K. Yang: Potentially Stably
Rational del Pezzo Surfaces Over Nonclosed Fields.
Melvyn B. Nathanson is a Professor of Mathematics at the City University of New York.