Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016 (Springer Proceedings in Mathematics & Statistics, 220)

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.#xE022 Front Matter ....Pages i-viii 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 Open Problems About Sumsets in Finite Abelian Groups: Minimum Sizes and Critical Numbers (Béla Bajnok)....Pages 9-23 Benford Behavior of Generalized Zeckendorf Decompositions (Andrew Best, Patrick Dynes, Xixi Edelsbrunner, Brian McDonald, Steven J. Miller, Kimsy Tor et al.)....Pages 25-37 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 Recurrence Identities of b-ary Partitions (Dakota Blair)....Pages 53-83 Cryptographic Hash Functions and Some Applications to Information Security (Lisa Bromberg)....Pages 85-97 Numerical Sets, Core Partitions, and Integer Points in Polytopes (Hannah Constantin, Ben Houston-Edwards, Nathan Kaplan)....Pages 99-127 Pairs of Dot Products in Finite Fields and Rings (David Covert, Steven Senger)....Pages 129-138 Characteristic, Counting, and Representation Functions Characterized (Charles Helou)....Pages 139-155 Partitions into Parts Simultaneously Regular, Distinct, And/or Flat (William J. Keith)....Pages 157-170 White’s Theorem (Mizan R. Khan, Karen M. Rogers)....Pages 171-180 A Misère-Play \(\star \)-Operator (Matthieu Dufour, Silvia Heubach, Urban Larsson)....Pages 181-198 A New Proof of Khovanskiĭ’s Theorem on the Geometry of Sumsets (Jaewoo Lee)....Pages 199-204 Initial Sums of the Legendre Symbol: Is \(\min + \max \ge 0\) ? (Kieren MacMillan, Jonathan Sondow)....Pages 205-213 A Second Wave of Expanders in Finite Fields (Brendan Murphy, Giorgis Petridis)....Pages 215-238 Sumsets Contained in Sets of Upper Banach Density 1 (Melvyn B. Nathanson)....Pages 239-248 The Erdős Paradox (Melvyn B. Nathanson)....Pages 249-254 Limits and Decomposition of de Bruijn’s Additive Systems (Melvyn B. Nathanson)....Pages 255-267 Extending Babbage’s (Non-)Primality Tests (Jonathan Sondow)....Pages 269-277 Conjectures on Representations Involving Primes (Zhi-Wei Sun)....Pages 279-310