发表机构
University of Arizona（亚利桑那大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明加法阿贝尔群无大小为5的MSTD集，借助计算机程序完成任意域中6-9大小MSTD集的分类，并探究Z/pZ乘法子群中MSTD集的最小基数。
AI 中文摘要
加法阿贝尔群中的有限集A，若满足|A+A|>|A−A|，则称为More Sums Than Differences（MSTD）集。我们证明加法阿贝尔群中不存在大小为5的MSTD集；随后借助受Hegarty启发的计算机程序，得到任意域中大小为6、7、8、9的MSTD集的分类结果，还研究了Z/pZ的乘法子群中MSTD集的最小基数。
英文摘要
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 $\Z/p\Z$.
CommentsPaper is first 25 pages, the rest is the appendix. Code is available at: https://github.com/yorickherrmann-star/Code-for-Small-MSTD-Sets-in-Arbitrary-Fields
