# 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} }

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 Sets Can and Cannot Have Sum-Dominant Subsets

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## When Almost All Sets Are Difference Dominated in Z/nZ

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