Peter Hegarty
Published 2006-11-19, updated 2007-01-05Version 2
We present a variety of new results on finite sets A of integers for which the sumset A+A is larger than the difference set A-A, so-called MSTD (more sums than differences) sets. First we show that there is, up to affine transformation, a unique MSTD subset of {\bf Z} of size 8. Secondly, starting from some examples of size 9, we present several new constructions of infinite families of MSTD sets. Thirdly we show that for every fixed ordered pair of non-negative integers (j,k), as n -> \infty a positive proportion of the subsets of {0,1,2,...,n} satisfy |A+A| = (2n+1) - j, |A-A| = (2n+1) - 2k.
Comments: 21 pages, no figures. Section 4 has been rewritten and Theorem 8 is a strengthening of Theorem 9 in previous version. Reference list updated, plus some other cosmetic changes
Explicit constructions of infinite families of MSTD sets
Explicit constructions of extractors and expanders
Explicit Constructions of the non-Abelian $\mathbf{p^3}$-Extensions Over $\mathbf{\QQ}$
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