Steven J. Miller, Brooke Orosz, Daniel Scheinerman
Published 2008-09-26, updated 2008-11-22Version 2
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}.
Comments: Version 2: 14 pages, 1 figure. Includes extensions to ternary forms and a conjecture for general combinations of the form Sum_i epsilon_i A with epsilon_i in {-1,1} (would be a theorem if we could find a set to start the induction in general)
Journal: Journal of Number Theory 130 (2010) 1221--1233
Some explicit constructions of sets with more sums than differences
Explicit Constructions of the non-Abelian $\mathbf{p^3}$-Extensions Over $\mathbf{\QQ}$
On Sets with More Products than Quotients
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