Glicci simplicial complexes
Glicci simplicial complexes
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DOI：
10.1016/j.jpaa.2008.03.005
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发表时间：
2007-04
影响因子：
0.8
通讯作者：
U. Nagel;Tim Roemer
中科院分区：
文献类型：
--
作者：
U. Nagel;Tim Roemer
这是一个案例研究的潜力联络理论的方法，在组合数学的应用。联络论中的一个主要问题是多项式环中的齐次Cohen-Macaulay理想是否是glicci，即是否在完全交的G-联络类中。对于由弱顶点可分解的单纯复形定义的Stanley-Reisner理想，我们给出了肯定的回答。这类复形分别包括拟阵、移位复形和Gorenstein复形。此外，我们还构造了一个单纯复形，证明了它的glicci性质依赖于基场的性质。作为我们的方法的应用，我们建立了新的证据，斯坦利的两个可分割的配合物和斯坦利分解。
This note is a case study for the potential of liaison-theoretic methods to applications in Combinatorics. One of the main open questions in liaison theory is whether every homogeneous Cohen–Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the G-liaison class of a complete intersection. We give an affirmative answer to this question for Stanley–Reisner ideals defined by simplicial complexes that are weakly vertex-decomposable. This class of complexes includes matroid, shifted and Gorenstein complexes respectively. Moreover, we construct a simplicial complex which shows that the property of being glicci depends on the characteristic of the base field. As an application of our methods we establish new evidence for two conjectures of Stanley on partitionable complexes and Stanley decompositions.