Year: 2026
Type: preprint
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 $\Z/p\Z$.
Source: arXiv (Cornell University)
Author: Herrmann, Yorick
Institution: University of Arizona
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204185638