场的相关常数
The correlation constant of a field
摘要：
我们研究的相关性的边缘，向量或元素是在一个随机选择的生成树或基础，分别。在这里，我们遵循Huh和Wang的指导方针，引入一个不变量作为度量，称为图、向量配置、拟阵或场的相关常数。从他们的一个结果可以看出，这些相关常数是介于$0$和$2$之间的数。在这里，我们证明了每个场的相关常数至少是$\frac{8}{7}$。在我们的证明中，我们明确地构造向量配置和拟阵的正相关元素。
英文摘要：
We study the correlation of edges, vectors or elements to be in a randomly chosen spanning tree or a basis, respectively. Here we follow the guideline of Huh and Wang and introduce as a measure an invariant that is called the correlation constant of a graph, vector configuration, matroid or field. It follows from one of their results that these correlation constants are numbers between $0$ and $2$. Here, we show that the correlation constant of every field is at least $\frac{8}{7}$. In our proof we explicitly construct vector configurations and matroids with positively correlated elements.
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