Combinatorial and Additive Number Theory III: CANT, New York, USA, 2017 and 2018 (Springer Proceedings in Mathematics & Statistics, 297)

"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. ." - Prové de l'editor Front Matter ....Pages i-viii Weighted Zero-Sums for Some Finite Abelian Groups of Higher Ranks (S. D. Adhikari, Bidisha Roy, Subha Sarkar)....Pages 1-12 Counting Monogenic Cubic Orders (Shabnam Akhtari)....Pages 13-24 The Zeckendorf Game (Paul Baird-Smith, Alyssa Epstein, Kristen Flint, Steven J. Miller)....Pages 25-38 Iterated Riesel and Iterated Sierpiński Numbers (Holly Paige Chaos, Carrie E. Finch-Smith)....Pages 39-54 A General Framework for Studying Finite Rainbow Configurations (Mike Desgrottes, Steven Senger, David Soukup, Renjun Zhu)....Pages 55-63 Translation Invariant Filters and van der Waerden’s Theorem (Mauro Di Nasso)....Pages 65-74 Central Values for Clebsch–Gordan Coefficients (Robert W. Donley Jr.)....Pages 75-100 Numerical Semigroups Generated by Squares and Cubes of Three Consecutive Integers (Leonid G. Fel)....Pages 101-121 On Supra-SIM Sets of Natural Numbers (Isaac Goldbring, Steven Leth)....Pages 123-132 Mean Row Values in (u, v)-Calkin–Wilf Trees (Sandie Han, Ariane M. Masuda, Satyanand Singh, Johann Thiel)....Pages 133-146 Dimensions of Monomial Varieties (Melvyn B. Nathanson)....Pages 147-160 Matrix Scaling Limits in Finitely Many Iterations (Melvyn B. Nathanson)....Pages 161-167 Not All Groups Are LEF Groups, or Can You Know If a Group Is Infinite? (Melvyn B. Nathanson)....Pages 169-174 Binary Quadratic Forms in Difference Sets (Alex Rice)....Pages 175-196 Egyptian Fractions, Nonstandard Extensions of \(\mathbb R\), and Some Diophantine Equations Without Many Solutions (David A. Ross)....Pages 197-207 A Dual-Radix Approach to Steiner’s 1-Cycle Theorem (Andrey Rukhin)....Pages 209-226 Potentially Stably Rational Del Pezzo Surfaces over Nonclosed Fields (Yuri Tschinkel, Kaiqi Yang)....Pages 227-233