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, Archit Kulkarni, +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

    Figures from this paper.

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 14 REFERENCES