论文标题
链接的球包装
Ball packings for links
论文作者
论文摘要
由$ ball（l）$表示的链接$ l $的球号是实现代表$ l $的项链所需的最小固体球（不一定是相同尺寸）。在本文中，我们表明$ ball（l）\ leq 5 cr（l）$，其中$ cr（l）$表示$ l $的交叉数。为此，我们使用用于球包装的Lorentz几何形状。著名的Koebe Andreev-Thurston圆圈包装定理也是证明的重要砖头。我们的方法屈服于算法，以在3维空间中明确构建$ l $的项链表示。
The ball number of a link $L$, denoted by $ball(L)$, is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing $L$. In this paper, we show that $ball(L)\leq 5 cr(L)$ where $cr(L)$ denotes the crossing number of $L$. To this end, we use Lorentz geometry applied to ball packings. The well-known Koebe-Andreev-Thurston circle packing Theorem is also an important brick for the proof. Our approach yields to an algorithm to construct explicitly the desired necklace representation of $L$ in the 3-dimensional space.
