Abstract
An MSTD set is a finite set with more pairwise sums than differences. $(\Upsilon,\Phi)$-ismorphisms are generalizations of Freiman isomorphisms to arbitrary linear forms. These generalized isomorphisms are used to prove that every finite set of real numbers is Freiman isomorphic to a finite set of integers. This implies that there exists no MSTD set $A$ of real numbers with $|A| \leq 7$, and, up to Freiman isomorphism and affine isomorphism, there exists exactly one MSTD set $A$ of real numbers with $|A| = 8$.
Citation
Melvyn B. Nathanson. "MSTD sets and Freiman isomorphisms." Funct. Approx. Comment. Math. 58 (2) 187 - 205, June 2018. https://doi.org/10.7169/facm/1685
Information