Abstract.
A More Sums Than Differences (MSTD) set is a set of integers
whose sumset is larger than its difference set . While it is known that as a positive percentage of subsets of are MSTD sets, the methods to prove this are probabilistic and do not yield nice, explicit constructions. Recently Miller, Orosz and Scheinerman (2010) gave explicit constructions of a large family of MSTD sets; though their density is less than a positive percentage, their family's density among subsets of is at least for some , significantly larger than the previous constructions, which were on the order of . We generalize their method and explicitly construct a large family of sets A with . The additional sums and differences allow us greater freedom than by Miller, Orosz and Scheinerman (2010), and we find that for any the density of such sets is at least . In the course of constructing such sets we find that for any integer k there is an A such that , and show that the minimum span of such a set is 30.
© 2012 by Walter de Gruyter Berlin Boston