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We explicitly construct infinite families of MSTD (more sums than differences) sets, i.e., sets where |A+A|>|A−A|. There are enough of these sets to prove that there exists a constant C such that at least C/r4 of the 2r subsets of {1,…,r} are MSTD sets; thus our family is significantly denser than previous constructions (whose densities are at most f(r)/2r/2 for some polynomial f(r)). We conclude...
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