非循环与邻接安排及Linhart的一个猜测

ACYCLIC AND NEIGHBORINE ARRANGEMENTS AND A CONJECTURE OF LINHART

首先给出两类特殊的半球面安排和半平面安排，即非循环安排和邻接安排的定义；得到了它们的参数满足的一些方程．在此基础上，证明了J．Linhart关于半平面安排中权不超过k的面的个数的上界的猜测．

In this paper, the definitions of acyclic and neighboring arrangements are given. Sevenal equations and inequalities on parameters in these arrangements are proved. On these basis, the conjecture of J. Linhart is proved, which gives the upper bound of numbers of faces with weights not greater than k in arrangements of half planes.