广义五边形几何
Generalized pentagonal geometries
摘要：
五边形几何PENT（$k$，$r$）是部分线性空间，其中每条线与$k$点关联，每个点与$r$线关联，并且对于每个点$x$，存在与不与$x$共线的那些点精确关联的线。在这里，我们推广的概念，允许点不与$x$共线，以形成点集的施泰纳系统$S(2,k,w)$的块是线的几何。
英文摘要：
A pentagonal geometry PENT($k$, $r$) is a partial linear space, where every line is incident with $k$ points, every point is incident with $r$ lines, and for each point $x$, there is a line incident with precisely those points that are not collinear with $x$. Here we generalize the concept by allowing the points not collinear with $x$ to form the point set of a Steiner system $S(2,k,w)$ whose blocks are lines of the geometry.
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。
