A Geometric Perspective on the MSTD Question

  title={A Geometric Perspective on the MSTD Question},
  author={Steven J. Miller and Carsten Peterson},
  journal={Discrete \& Computational Geometry},
A more sums than differences (MSTD) set A is a subset of $$\mathbb {Z}$$Z for which $$|A+A| > |A-A|$$|A+A|>|A-A|. Martin and O’Bryant used probabilistic techniques to prove that a non-vanishing proportion of subsets of $$\{1, \dots , n\}$${1,⋯,n} are MSTD as $$n \rightarrow \infty $$n→∞. However, to date only a handful of explicit constructions of MSTD sets are known. We study finite collections of disjoint intervals on the real line, $$\mathbb {I}$$I, and explore the MSTD question for such… 
2 Citations
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  • J. Marica
  • Mathematics
    Canadian Mathematical Bulletin
  • 1969
Problem 7 of Section VI of H. T. Croft's "Research Problems" (August, 1967 edition) is by J. H. Conway: A is a finite set of integers {ai}. A + A denotes {ai + aj}, A - A denotes {ai - aj}. Prove