论 Freedman 的链环填装
On Freedman's link packings
AI总结：
本文研究 Freedman 提出的链环填装问题，证明其最小上界是精确的，并构造了任意链环的指数级填装，同时给出改进和推广的上界。
摘要：
最近，Freedman [arXiv:2301.00295] 提出了在几何约束下将最大数量的链环填装到有界区域中的思想，并在某些情形下给出了填装数的上界，同时指出这些界似乎过大。我们证明，这些“大得离谱”的界中最小的一个实际上是精确的，方法是针对任意链环，构造出数量随可用体积呈指数增长的多个副本的填装。我们还给出了改进且推广的上界。
英文摘要：
Recently, Freedman [arXiv:2301.00295] introduced the idea of packing a maximal number of links into a bounded region subject to geometric constraints, and produced upper bounds on the packing number in some cases, while commenting that these bounds seemed far too large. We show that the smallest of these "extravagantly large" bounds is in fact sharp by constructing, for any link, a packing of exponentially many copies as a function of the available volume. We also produce improved and generalized upper bounds.
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