发表机构
Drexel University（德雷塞尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明对称数值半群的间隙多项式临界点幂和对所有g∈G为零，伪对称数值半群删去z^{F/2}后结论成立，还得出临界值之和为零的推论。
AI 中文摘要
对于具有弗罗贝尼乌斯数F和间隙G的数值半群S，定义次数为F的间隙多项式P(z)为∑_{g∈G}c_g z^g。我们证明，对于对称数值半群，其间隙多项式临界点的幂和对每个幂g∈G均为零；对于伪对称数值半群，若从P(z)中也删去项z^{F/2}，则该结论同样成立。我们给出若干推论，包括间隙多项式的临界值之和为零这一事实。
英文摘要
For a numerical semigroup $S$ with Frobenius number $F$ and gaps $G$, a polynomial $P\left(z\right)=\sum_{g\in G}c_{g}z^{g}$ of degree $F$ is called a gap polynomial. We show that for a symmetric numerical semigroup, the power sums of the critical points of a gap polynomial vanish for every power $g\in G$. For a pseudo-symmetric numerical semigroup, the same result holds if the term $z^{F/2}$ is omitted from $P\left( z\right) $. We give several corollaries, including that the sum of the critical values of a gap polynomial vanishes.
