## Functiones et Approximatio Commentarii Mathematici

### MSTD sets and Freiman isomorphisms

Melvyn B. Nathanson

#### 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 $|A| = 8$.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 58, Number 2 (2018), 187-205.

Dates
First available in Project Euclid: 2 December 2017

https://projecteuclid.org/euclid.facm/1512183760

Digital Object Identifier
doi:10.7169/facm/1685

Mathematical Reviews number (MathSciNet)
MR3816073

Zentralblatt MATH identifier
06924926

#### Citation

Nathanson, Melvyn B. MSTD sets and Freiman isomorphisms. Funct. Approx. Comment. Math. 58 (2018), no. 2, 187--205. doi:10.7169/facm/1685. https://projecteuclid.org/euclid.facm/1512183760

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