Constructing MSTD Sets Using Bidirectional Ballot Sequences

A more sums than differences (MSTD) set is a finite subset S of the integers such that |S+S| > |S-S|. We construct a new dense family of MSTD subsets of {0, 1, 2, …, n-1}. Our construction gives Theta(2^n/n) MSTD sets, improving the previous best construction with Omega(2^n/n^4) MSTD sets by Miller, Orosz, and Scheinerman.