Combinatorial and Additive Number Theory VII
Description
This book finds peer-reviewed and edited papers on current topics in number theory. This book, the seventh in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 22nd and 23rd annual workshops, held in New York in 2024 and 2025, respectively. Organized every year since 2003 by Mel Nathanson at the CUNY Graduate Center, the workshops survey state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics.
This selection of articles is of relevance to both researchers and graduate students interested in current progress in number theory.
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Content
Visibiiity in the plane for function fields.- On a pair of diophantine equations.- A combinatorial introduction to Adinkras.- Ratio between a sum of generators and rational powers of their product in numerical semigroups and Wilf's question.- Constructions of sequences of alternating sum and difference dominated sets.- Lp averages of the discrete Fourier transform and applications.- Limiting behavior of resistances in triangular graphs.- Scaled Arndt Compositions.- Petersson-Knopp type identities for generalized Dedekind and Hardy-Berndt sums involving Apostol-Bernoulli functions.- Limiting behavior in missing sums of sumsets.- Multi-parameter Szemer´edi-Trotter-type theorems and applications in finite fields.- Arithmetic functions that remain constant on runs of consecutive integers.- Gauss's proof of Descartes's rule of signs.- Poincar´e's Positivstellensatz.- Polytopes, polyhedra, and the Farkas lemma.- Visualizing the sum-product conjecture.- An Unsure Note on an Un-Schur Problem.- A note on iterated sumset races.- Egyptian fractions on groups.