Arrangements of pseudolines are classic objects in discrete and computational geometry. They have been studied with increasing intensity since their introduction almost 100 years ago. The study of the number $B_n$ of non-isomorphic simple arrangements of $n$ pseudolines goes back to Goodman and Pollack, Knuth, and others. It is known that $B_n$ is in the order of $2^{\Theta(n^2)}$ and finding asymptotic bounds on $b_n = \frac{\log_2(B_n)}{n^2}$ remains a challenging task. In 2011, Felsner and Valtr showed that $0.1887 \leq b_n \le 0.6571$ for sufficiently large $n$. The upper bound remains untouched but in 2020 Dumitrescu and Mandal improved the lower bound constant to $0.2083$. Their approach utilizes the known values of $B_n$ for up to $n=12$. We tackle the lower bound by utilizing dynamic programming and the Lindstr\"om-Gessel-Viennot lemma. Our new bound is $b_n \geq 0.2721$ for sufficiently large $n$. The result is based on a delicate interplay of theoretical ideas and computer assistance.

翻译：伪线排列是离散与计算几何中的经典对象，自约百年前被引入以来，其研究强度持续增长。对$n$条伪线的非同构简单排列数$B_n$的研究可追溯到Goodman、Pollack、Knuth等人。已知$B_n$的阶为$2^{\Theta(n^2)}$，而为$b_n = \frac{\log_2(B_n)}{n^2}$寻找渐近界仍是一项具有挑战性的任务。2011年，Felsner与Valtr证明对充分大的$n$有$0.1887 \leq b_n \leq 0.6571$。上界迄今未被突破，但2020年Dumitrescu与Mandal将下界常数改进至$0.2083$，其方法利用了$n \leq 12$时$B_n$的已知值。我们通过动态规划与Lindström-Gessel-Viennot引理攻克下界问题，得到对充分大$n$有$b_n \geq 0.2721$的新界。该结果基于理论思想与计算机辅助的精细互动。