A Classification of Small MSTD Sets in Arbitrary Fields
Yorick Herrmann
Abstract
A finite set A in an additive abelian group is a More Sums Than Differences (MSTD) set if |A+A| > |A-A|. We prove that no MSTD set of size 5 exists in an additive abelian group. Using a computer program inspired by Hegarty, we then obtain classifications of MSTD sets of sizes 6, 7, 8, and 9 in arbitrary fields. We also investigate the minimal cardinality of MSTD sets that are multiplicative subgroups of /p.
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