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arXiv · 1609.04578

MSTD sets and Freiman isomorphisms

Melvyn B. Nathanson
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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, there exists exactly one MSTD set $A$ of real numbers with $|A| = 8$.

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Melvyn B. Nathanson. 2016-09-15. MSTD sets and Freiman isomorphisms. https://arxiv.org/abs/1609.04578

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