论文标题
仿射成绩单的热带临界点
The tropical critical points of an affine matroid
论文作者
论文摘要
我们证明，仿射基质（M，e）的热带临界点数等于M.的β不变性M.由计算最大似然度的计算而动机，该数字被定义为（M，e）的Bergman粉丝的相互作用程度（M，E）和nvered Bergman and n =（m/e）col a col an col n lo是一个元素*，而不是一个元素。等效地，对于E-E上的通用权重向量w，这是在N上找到重量（0，x）在N上的M和Y上的方法的数量，以便在M（resp。N）的每个电路上，最小X-Weight（分别为Y-Weight）至少出现二次。这回答了sturmfels的问题。
We prove that the number of tropical critical points of an affine matroid (M,e) is equal to the beta invariant of M. Motivated by the computation of maximum likelihood degrees, this number is defined to be the degree of the intersection of the Bergman fan of (M,e) and the inverted Bergman fan of N=(M/e)*, where e is an element of M that is neither a loop nor a coloop. Equivalently, for a generic weight vector w on E-e, this is the number of ways to find weights (0,x) on M and y on N with x+y=w such that on each circuit of M (resp. N), the minimum x-weight (resp. y-weight) occurs at least twice. This answers a question of Sturmfels.
