Categorifying the magnitude of a graph
Categorifying the magnitude of a graph
复制标题
对图的大小进行分类
DOI：
10.4310/hha.2017.v19.n2.a3
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
S. Willerton
中科院分区：
文献类型：
--
作者：
Richard Hepworth;S. Willerton
图的大小可以被认为是与图相关的整数幂级数; Leinster使用他的度量空间大小的想法介绍了它。在这里，我们介绍了一个双阶同调理论的图，它的阶化欧拉特征的大小。这是一个量级的分类，其精神与霍瓦诺夫同调是琼斯多项式的分类相同。我们展示了如何性质的大小证明Leinster归类的性质，如Kunneth定理和迈耶-Vietoris定理。证明了图的联的同调是在对角线上支撑的。最后给出了各种计算机计算实例。
The magnitude of a graph can be thought of as an integer power series associated to a graph; Leinster introduced it using his idea of magnitude of a metric space. Here we introduce a bigraded homology theory for graphs which has the magnitude as its graded Euler characteristic. This is a categorification of the magnitude in the same spirit as Khovanov homology is a categorification of the Jones polynomial. We show how properties of magnitude proved by Leinster categorify to properties such as a Kunneth Theorem and a Mayer-Vietoris Theorem. We prove that joins of graphs have their homology supported on the diagonal. Finally, we give various computer calculated examples.
关于欧几里德空间子集的渐近幅
影响因子：
0.5
作者：
Leinster T
通讯作者：
Leinster T
影响因子：
0.9
作者：
Leinster T
通讯作者：
Leinster T