论文标题
较高订单的配置
Configurations of higher orders
论文作者
论文摘要
本文首先将点和行的组合配置的概念扩展到了点和平面的组合配置，我们称为订单$ 2 $的配置。然后，我们继续研究积分概念和$ k $ - 平面（$ k $二维超平面）的概念，我们称为订单$ k $的配置。我们提供了许多一般示例，例如订单$ k $的堆叠配置 - 直观地分层较低订单配置 - 以及订单$ k $的产品配置。我们讨论了标准配置的许多类似物，例如双重配置，同构，图形表示以及何时配置为几何。我们主要集中在订单$ 2 $的配置上，并专门计算订单$ 2 $的可能的对称配置数量，当每平面包含$ n $上的小值的$ 3 $点 - 配置中的积分总数。
This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further extension to the notion of points and $k$-planes ($k$-dimensional hyperplanes) which we refer to as configurations of order $k$. We present a number of general examples such as stacked configurations of order $k$ - intuitively layering lower order configurations - and product configurations of order $k$. We discuss many analogues of standard configurations such as dual configurations, isomorphisms, graphical representations, and when a configuration is geometric. We focus mostly on configurations of order $2$ and specifically compute the number of possible symmetric configurations of order $2$ when each plane contains $3$ points for small values on $n$ - the total number of points in the configuration.
