Based on talks from the 2015 and 2016 CANT workshops at the City University of New York, these proceedings offer 19 peer-reviewed and edited papers on current topics in number theory. The volume features subjects such as sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography. Held every year since 2003, this workshop series aims to survey state-of-the-art, open problems, and future colleagues of combinatorial and additive number theory and related parts of mathematics. Each contribution in this volume is dedicated to a specific topic and reflects the latest results by eminent experts in the field. Researchers and graduate students interested in the latest progress in number theory will find this selection of articles relevant and compelling.
1. Sukumar Das Adhikari and Shalom Eliahou, "On a conjecture of Fox
and Kleitman on the degree of regularity of a certain linear equation".-
2. Béla Bajnok, \Open problems about sumsets in finite abelian groups:
Minimum sizes and critical numbers".- 3. Andrew Best, Pat&rick Dynes, Xixi
Edelsbrunner, Brian McDonald, Steven J. Miller, Kimsy Tor, Caroline
Turnage-Butterbaugh and Madeleine Weinstein, "Benford behavior of generalized
Zeckendorf decompositions".- 4. Andrew Best, Karen Huan, Nathan McNew, Steven
J. Miller, Jasmine. Powell, Kimsy Tor, and Madeleine Weinstein, "Ramsey
theory problems over the integers: Avoiding generalized progressions".-
5. Dakota Blair, "Recurrence identities of b-ary partitions".- 6. Lisa
Bromberg, "Hashing with SL(2;Fp) and some applications to information
security".- 7. Hannah Constantin, Ben Houston-Edwards, and Nathan Kaplan,
"Numerical sets, core partitions, and integer points in polytopes".- 8. David
Covert and Steven Senger, "Pairs of dot products infinite fields and rings".-
9. Charles Helou, "Characteristic, counting, and representation functions.-
10.&nbWiln>liam J. Keith, \Partitions into parts simultaneously regular,
distinct, and/or flat".- 11. Mizan R. Khan and Karen M. Rogers, "An
exposition of White's characterization of empty lattice tetrahedra".-
12. Urban Larsson, \A misčere-play ?-operator".-
13. Jaewoo Lee, "A new proof
of Khovanski's theorem on the geometry of sumsets.- 14. >;Kieren MacMillan
and Jonathan Sondow, "Initial sums of the Legendre symbol: Is min+max 0 ?".-
15. Brendan Murphy and Giorgis Petridis, "A second wave of expanders in
finite fi elds".- 16. Melvyn B. Nathanson, "The Erd}os paradox".- 17. Melvyn
B. Nathanson, "Limits and decomposition of de Bruijn's additive systems".-
18. Jonathan Sondow, "Extending Babbage's (non-)primality tests".-
19. Zhi-Wei Sun, "Conjectures on representations involving primes".
Melvyn B. Nathanson is a Professor of Mathematics at the City University of New York.
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