几何排列中禁用模式的组合提升实验研究
An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting
摘要：
我们研究了在$\mathbb{R}^3$中判定一个给定的排列三元组是否可以实现为不相交凸集的几何排列的问题。我们表明，这个问题，这是相当于决定由三次多项式的某些半代数集的空虚，可以“解除”一个纯粹的组合问题。我们提出了一个有效的算法，并使用它来获得新的见解的几何排列的结构。
英文摘要：
We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in $\mathbb{R}^3$. We show that this question, which is equivalent to deciding the emptiness of certain semi-algebraic sets bounded by cubic polynomials, can be "lifted" to a purely combinatorial problem. We propose an effective algorithm for that problem, and use it to gain new insights into the structure of geometric permutations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
