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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

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)5cr(L) where cr(L) denotes the crossing number of a nontrivial nonsplittable link L. 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 L in R3.



中文翻译:

链接用球填料

链接的球数大号,表示为 b一种大号,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) 大号。在本文中,我们表明b一种大号5C[R大号 在哪里 C[R大号表示非平凡不可分割链接的交叉编号大号。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大号[R3

更新日期:2021-05-08
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