关于小规模网格中序型的个数
On the Number of Order Types in Integer Grids of Small Size
摘要：
设$\{p_1,\dots,p_n\}$和$\{q_1,\dots,q_n\}$是平面中一般位置上的两组$n$标记点。我们说这两个点集具有相同的序类型，如果对于每个索引三元组$(i,j,k)$，$p_k$在从$p_i$到$p_j$的有向线之上当且仅当$q_k$在从$q_i$到$q_j$的有向线之上。本文给出了多项式整数网格上可实现的不同阶类型的$n$点个数的第一非平凡下界
英文摘要：
Let $\{p_1,\dots,p_n\}$ and $\{q_1,\dots,q_n\}$ be two sets of $n$ labeled points in general position in the plane. We say that these two point sets have the same order type if for every triple of indices $(i,j,k)$, $p_k$ is above the directed line from $p_i$ to $p_j$ if and only if $q_k$ is above the directed line from $q_i$ to $q_j$. In this paper we give the first non-trivial lower bounds on the number of different order types of $n$ points that can be realized in integer grids of polynomial
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。
