嵌入维数为4的数值半群极小表示的类型与基数
The type and cardinality of minimal presentations of numerical semigroups with embedding dimension four
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中文总结 AI 辅助
该研究针对嵌入维数为4的数值半群，借助Apéry集几何方法推导了其类型与极小表示基数间的新不等式界，解决了相关公开问题并改进了已有界值。
中文摘要 AI 辅助
针对嵌入维数为4的数值半群$S$，我们研究其类型$t(S)$与极小表示基数$η(S)$之间的关系。采用基于Apéry集几何的方法，我们证明了$4t(S) + 5 \geq η(S) \geq t(S)-11$。这解决了Moscariello与Sammartano提出的$t(S)$是否可由$η(S)$的函数界定的问题，同时改进了Bresinsky此前给出的界$9t(S) + 4 \geq η(S)$。
英文摘要
For a numerical semigroup $S$ with embedding dimension four, we study the relationship between its type $t(S)$ and the cardinality of its minimal presentations $η(S)$. Using an approach based on the geometry of the Apéry set, we prove that $4t(S) + 5 \geq η(S) \geq t(S)-11$. This resolves a problem of Moscariello and Sammartano asking whether $t(S)$ is bounded by a function of $η(S)$, and improves the previously known bound $9t(S) + 4 \geq η(S)$ due to Bresinsky.
