Betti numbers of toric ideals of graphs: A case study
Betti numbers of toric ideals of graphs: A case study
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图的环面理想的 Betti 数：案例研究
DOI：
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发表时间：
2018
影响因子：
0.8
通讯作者：
M. E. U. Paczka
中科院分区：
文献类型：
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作者：
Federico Galetto;Johannes Hofscheier;Graham Keiper;C. Kohne;Adam Van Tuyl;M. E. U. Paczka
本文计算了一类图的环面理想的分次Betti数。关键的观察是，这个家庭承认一个初始理想，其中有线性矩阵。作为一个推论，我们计算希尔伯特级数和[公式：见正文]-向量的所有环面理想的图在这个家庭。
We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this family admits an initial ideal which has linear quotients. As a corollary, we compute the Hilbert series and [Formula: see text]-vector for all the toric ideals of graphs in this family.