论文标题
改进的斐波那契晶格的分散范围
Improved dispersion bounds for modified Fibonacci lattices
论文作者
论文摘要
我们研究单位正方形中点集的分散。即，在这样的点集中，最大的轴并行盒的大小。 It is known that $\liminf_{N\to\infty} N\mathrm{disp}(N,2)\in \left[\frac54,2\right],$ where $\mathrm{disp}(N,2)$ is the minimal possible dispersion for an $N$-element point set in the unit square.上限2通过显式点构造获得 - 众所周知的斐波那契晶格。在本文中，我们发现对该点集的修改，使其分散体显着低于斐波那契晶格的分散体。我们的主要结果将暗示$ \ liminf_ {n \ to \ infty} n \ mathrm {disp}（n，2）\ leq leq或sqrt {5} = 1.894427 ... $
We study the dispersion of point sets in the unit square; i.e. the size of the largest axes-parallel box amidst such point sets. It is known that $\liminf_{N\to\infty} N\mathrm{disp}(N,2)\in \left[\frac54,2\right],$ where $\mathrm{disp}(N,2)$ is the minimal possible dispersion for an $N$-element point set in the unit square. The upper bound 2 is obtained by an explicit point construction - the well-known Fibonacci lattice. In this paper we find a modification of this point set such that its dispersion is significantly lower than the dispersion of the Fibonacci lattice. Our main result will imply that $\liminf_{N\to\infty} N\mathrm{disp}(N,2)\leq φ^3/\sqrt{5}=1.894427...$
