论文标题
从矩形到生根的树以及其他
Activity from matroids to rooted trees and beyond
论文作者
论文摘要
基金会碱基的内部和外部活性是众所周知的概念，例如，人们可以定义Tutte多项式。最近，我们发现了增益超平面排列区域与有色标签的生根树之间的对应关系。在这里，我们定义了一种一般活动理论，该理论特别适用于无破碎的电路（NBC）集和标记为彩色树。活动的特殊情况\ textsf {0}是我们的激励案例。结果，在增益超平面排列中，有限区域的数量等于相应的彩色标记的活动\ textsf {0}的标记的生根树。
The interior and exterior activities of bases of a matroid are well-known notions that for instance permit one to define the Tutte polynomial. Recently, we have discovered correspondences between the regions of gainic hyperplane arrangements and coloredlabeled rooted trees. Here we define a general activity theory that applies in particular to no-broken circuit (NBC) sets and labeled colored trees. The special case of activity \textsf{0} was our motivating case. As a consequence, in a gainic hyperplane arrangement the number of bounded regions is equal to the number of the corresponding colored labeled rooted trees of activity \textsf{0}.
