Melvyn B. Nathanson 
Combinatorial and Additive Number Theory III [PDF ebook] 
CANT, New York, USA, 2017 and 2018

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. 

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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. Di Nasso: 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.

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