关于广义二项式边理想的希尔伯特级数和重数
On the Hilbert Series and Multiplicity of Generalized Binomial Edge Ideals
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中文总结 AI 辅助
本文计算了图的联结及完全r-部图的广义二项式边理想的希尔伯特级数，并给出顶点移除下系数不变的约简技术，进而计算几类图的维数和重数。
中文摘要 AI 辅助
本文计算了与两个图的联结相关的广义二项式边理想的希尔伯特级数。因此，我们计算了完全$r$-部图的希尔伯特级数。进一步，我们证明如果某个顶点满足一定的度条件，则移除该顶点后某些希尔伯特系数保持不变。这为计算这些系数提供了一种约简技术。作为应用，我们计算了几类图的维数和重数。
英文摘要
In this article, we compute the Hilbert series of the generalized binomial edge ideal associated with the join of two graphs. Consequently, we compute the Hilbert series of complete $r$-partite graphs. Further, we show that if a vertex satisfies a certain degree condition, then some Hilbert coefficients remain unchanged upon its removal. This provides a reduction technique for computing them. As an application, we compute the dimension and multiplicity of several classes of graphs.
发表机构
- Indian Institute of Technology, Jammu（印度技术学院詹姆分校）
机构由 AI 辅助整理，请以论文原文为准。
