发表机构
Charles University; Universidad Autónoma del Estado de Hidalgo; Universidad Autónoma de San Luis Potosí（查理大学; 伊达尔戈自治大学; 圣路易斯波托西自治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明对每个$m\ge 3$，大小为$m$的不可避免的简单$k$-伪直线排列数量随$k$指数增长，且对偶数$k$，伪圆的$k$-排列也有类似结果。
AI 中文摘要
伪直线的$k$-排列是平面上一组双无限曲线，使得任意两条曲线恰好相交于$k$个点，且在这些点处交叉；如果没有三条曲线交于同一点，则称为简单的。循环排列是唯一不可避免的简单$1$-伪直线排列，在拉姆齐意义上：对于每个固定的$m\ge 1$，每个足够大的简单$1$-伪直线排列都有一个大小为$m$的循环子排列。我们证明，对于每个$m\ge 3$，大小为$m$的不可避免的简单$k$-伪直线排列的数量随$k$指数增长，且与$m$无关。对于偶数$k$，我们证明了伪圆的$k$-排列的类似结果。
英文摘要
A $k$-arrangement of pseudolines is a set of bi-infinite curves in the plane such that any two of them intersect each other in exactly $k$ points, at which they cross, and it is simple if no three curves meet at a common point. Cyclic arrangements are the only simple $1$-arrangements of pseudolines that are unavoidable, in the Ramsey spirit: for each fixed $m\ge 1$, every sufficiently large simple $1$-arrangement of pseudolines has a cyclic subarrangement of size $m$. We show that, for every $m\ge 3$, the number of unavoidable simple $k$-arrangements of pseudolines of size $m$ grows exponentially with $k$, independently of $m$. For even $k$, we prove an analogous result for $k$-arrangements of pseudocircles.
Comments19 pages, 10 figures
