An MSTD set is a finite set of integers with more sums than differences. It is proved that, for infinitely many positive integers $k$, there are infinitely many affinely inequivalent MSTD sets of cardinality $k$. There are several related open problems.
Comparison estimates for linear forms in additive number theory
Problems in additive number theory, VI: Sizes of sumsets
Every finite set of integers is an asymptotic approximate group
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