A Geometric Perspective on the MSTD Question

@article{Miller2019AGP,
title={A Geometric Perspective on the MSTD Question},
author={Steven J. Miller and Carsten Peterson},
journal={Discrete \& Computational Geometry},
year={2019},
pages={1-24}
}
• Published 2 September 2017
• Mathematics
• 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…
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