AI 中文总结
该研究提出算法枚举分类最大化三角面的奇数n条伪线简单排列，通过深度优先搜索结合几何剪枝实现，给出不同n的完整枚举结果及大n的部分结果，证明搜索分类的完整性。
AI 中文摘要
我们描述了用于穷举枚举和分类n条伪线（n为奇数）的简单排列的算法，这类排列能最大化三角面的数量。深度优先搜索仅通过对偶数索引的生成器分支来枚举最长置换w₀的简约字，并利用最优排列的几何结构施加剪枝约束。该方法可处理具有规则三角图案的完美排列，以及n≡1 mod 6时不可避免的偏离情况。输出被划分为等价类的层次结构：按交换关系、欧几里得变换和射影变换划分。对于每个射影类，我们恢复其完整对称群G⊆S_{n+1}以及欧几里得子类的轨道-稳定子轮廓。搜索和分类的完整性已被证明：每个布线图都能被访问。我们报告了完整的枚举结果；例如，当n=27时，有85,562,064个布线图被划分为56,646个射影类。对于更大的n（最大至n=93），穷举枚举无法实现，我们报告了部分（首次命中）结果。
英文摘要
We describe algorithms for the exhaustive enumeration and classification of simple arrangements of $n$ pseudolines ($n$ odd) maximizing the number of triangular faces. The depth-first search enumerates reduced words for the longest permutation $w_0$ by branching only on the even-indexed generators, using pruning constraints imposed by the geometry of optimal arrangements. The approach handles both perfect arrangements with a regular triangular pattern and unavoidable deviations from it for $n \equiv 1 \pmod 6$. The output is classified into a hierarchy of equivalence classes: by commutation, by Euclidean transformations, and by projective transformations. For each projective class we recover its full symmetry group $G \subseteq S_{n+1}$ together with the orbit-stabilizer profile of its Euclidean subclasses. Completeness of the search and classification is proved: every wiring diagram is reached. We report full enumerations; e.g. for $n=27$, 85,562,064 wiring diagrams partitioned into 56,646 projective classes. For larger $n$ (up to $n=93$), where exhaustive enumeration is out of reach, we report partial (first-hit) results.
Comments58 pages, 17 figures, 7 tables. Code and data: https://github.com/parpalak/pseudoline-algorithms
