论文标题
常规细分的MST-FAN
The MST-fan of a regular subdivision
论文作者
论文摘要
常规三角测量$σ（h）$的双图$γ（h）$具有自然公制结构。最近证明，最小跨越$γ（h）$的树木是在人口遗传学背景下检测重要数据信号的结论性。在本文中，我们证明了这种最小跨越树的参数空间被组织为多面体风扇，称为$σ（h）$的MST-Fan，该粉丝将$σ（H）$的次级锥体细分为参数锥。我们部分地描述了其本地面部结构，并根据Matroids和Bergman的粉丝研究了与热带几何形状的联系。
The dual graph $Γ(h)$ of a regular triangulation $Σ(h)$ carries a natural metric structure. The minimum spanning trees of $Γ(h)$ recently proved to be conclusive for detecting significant data signal in the context of population genetics. In this paper we prove that the parameter space of such minimum spanning trees is organized as a polyhedral fan, called the MST-fan of $Σ(h)$, which subdivides the secondary cone of $Σ(h)$ into parameter cones. We partially describe its local face structure and examine the connection to tropical geometry in virtue of matroids and Bergman fans.
