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Ball packings for links
European Journal of Combinatorics ( IF 1 ) Pub Date : 2021-05-08 , DOI: 10.1016/j.ejc.2021.103351 Jorge L. Ramírez Alfonsín , Iván Rasskin
中文翻译:
链接用球填料
更新日期:2021-05-08
European Journal of Combinatorics ( IF 1 ) Pub Date : 2021-05-08 , DOI: 10.1016/j.ejc.2021.103351 Jorge L. Ramírez Alfonsín , Iván Rasskin
The ball number of a link , denoted by , is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing . In this paper, we show that where denotes the crossing number of a nontrivial nonsplittable link . To this end, we use the connection of the Lorentz geometry with the ball packings. The well-known Koebe–Andreev–Thurston circle packing Theorem is also an important brick for the proof. Our approach yields an algorithm to construct explicitly the desired necklace representation of in .
中文翻译:
链接用球填料
链接的球数,表示为 ,是实现一条项链所需要的最少实心球数(不一定是相同大小) 。在本文中,我们表明 在哪里 表示非平凡不可分割链接的交叉编号。为此,我们使用洛伦兹几何形状与球填料的连接。著名的Koebe–Andreev–Thurston圆堆积定理也是证明的重要依据。我们的方法产生了一种算法,可以明确构造所需的项链表示 在 。