# Sets characterized by missing sums and differences in dilating polytopes

```@article{D2014SetsCB,
title={Sets characterized by missing sums and differences in dilating polytopes},
author={Thao D{\^o} and Archit Kulkarni and Steven J. Miller and David Moon and Jake L. Wellens and James Wilcox},
journal={Journal of Number Theory},
year={2014},
volume={157},
pages={123-153}
}```
• Thao Dô, +3 authors James Wilcox
• Published 2014
• Mathematics
• Journal of Number Theory
• A sum-dominant set is a finite set A of integers such that |A+A|>|A−A|. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed that the proportion of sum-dominant subsets of {0,…,n} is bounded below by a positive constant as n→∞. Hegarty then extended their work and showed that for any prescribed s,d ∈ N_0, the proportion P^(a,d)_n of subsets of {0,…,n} that are missing exactly s… CONTINUE READING

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## When almost all sets are difference dominated in \$\mathbb{Z}/n\mathbb{Z}\$

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## Problems in additive number theory, V: Affinely inequivalent MSTD sets

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## E-mail address: auk@andrew.cmu.edu DEPARTMENT OF MATHEMATICAL SCIENCES

• E-mail address: auk@andrew.cmu.edu DEPARTMENT OF MATHEMATICAL SCIENCES