Explicit constructions of infinite families of MSTD sets

TextWe explicitly construct infinite families of MSTD (more sums than differences) sets, i.e., sets where |A+A|>|A−A||A+A|>|A−A|. There are enough of these sets to prove that there exists a constant C   such that at least C/r4C/r4 of the r22r subsets of {1,…,r}{1,…,r} are MSTD sets; thus our family is significantly denser than previous constructions (whose densities are at most f(r)/2r/2f(r)/2r/2 for some polynomial f(r)f(r)). We conclude by generalizing our method to compare linear forms ϵ1A+⋯+ϵnAϵ1A+⋯+ϵnA with ϵi∈{−1,1}ϵi∈{−1,1}.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=vIDDa1R2.