Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 58, Number 2 (2018), 187-205.
MSTD sets and Freiman isomorphisms
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 $|A| = 8$.
Funct. Approx. Comment. Math., Volume 58, Number 2 (2018), 187-205.
First available in Project Euclid: 2 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11B13: Additive bases, including sumsets [See also 05B10]
Secondary: 11B75: Other combinatorial number theory 05B20: Matrices (incidence, Hadamard, etc.) 05A19: Combinatorial identities, bijective combinatorics 05A17: Partitions of integers [See also 11P81, 11P82, 11P83] 11D04: Linear equations
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