论文标题
线路排列中区域数量的注释
A Note on the Number of Regions in a Line Arrangement
论文作者
论文摘要
对于在实际投影平面中的$ n $行安排，我们用$ f $表示真正的投影平面由线划分的区域数量。使用Bojanowski的不平等，我们为$ f $建立了一个新的下限。特别是，我们表明，如果不超过$ \ frac {2} {3} n $ lines在任何时候相交，则$ f \ ge \ frac {1} {6} {6} n^{2} $
For an arrangement of $n$ lines in the real projective plane, we denote by $f$ the number of regions into which the real projective plane is divided by the lines. Using Bojanowski's inequality, we establish a new lower bound for $f$. In particular, we show that if no more than $\frac{2}{3}n$ lines intersect at any point, then $f \ge \frac{1}{6}n^{2}$
