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arXiv · 0809.4621

Explicit constructions of infinite families of MSTD sets

Steven J. Miller·Brooke Orosz·Daniel Scheinerman
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Abstract

We explicitly construct infinite families of MSTD (more sums than differences) sets. There are enough of these sets to prove that there exists a constant C such that at least C / r^4 of the 2^r subsets of {1,...,r} are MSTD sets; thus our family is significantly denser than previous constructions (whose densities are at most f(r)/2^{r/2} for some polynomial f(r)). We conclude by generalizing our method to compare linear forms epsilon_1 A + ... + epsilon_n A with epsilon_i in {-1,1}.

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Steven J. Miller, Brooke Orosz, Daniel Scheinerman. 2008-11-22. Explicit constructions of infinite families of MSTD sets. https://doi.org/10.1016/j.jnt.2009.09.003

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