AI 中文总结
本文证明平面线排列中，除两种特殊情况外，总存在一条线使某开半平面包含超过一半的有界胞腔，并探讨相关差异度问题。
AI 中文摘要
平面中 $n$ 条线的排列定义了胞腔，即排列补集的连通分量。回答 Volkmar Welker 的一个问题，我们证明：除两种特殊情况外，排列中总存在一条线 $L$，使得以 $L$ 为边界的某个开半平面包含该排列超过一半的有界胞腔。我们还考虑了与该问题相关的一些不寻常的差异度问题。
英文摘要
An arrangement of $n$ lines in the plane defines cells, i.e., connected components of the complement of the arrangement. Answering a question of Volkmar Welker we show that, apart from two special cases, there is always a line $L$ in the arrangement such that one of the open halfplanes whose boundary is $L$ contains more than half of the bounded cells of the arrangement. We also consider some unusual discrepancy problems that are related to this question.
