Explicit constructions of infinite families of MSTD sets Additive Number Theory: Festschrift

ABSTRACT. We explicitly construct infinite families of MSTD (more sums than differ-ences) 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 by general-izing our method to compare linear forms 1A+ · · ·+ nA with i ∈ {−1, 1}. 1