有趣的部分四边形集
Intriguing sets of partial quadrangles
摘要：
称为\textit{partial quadrangle}的点-线几何（由Cameron在1975年引入）具有这样的性质，即对于每个点/线非关联对$(P,\ell)$，最多有一条线通过$P$与$\ell$并发。特别是，被称为\textit{generalised quadrangles}的研究对象都是部分四边形。广义四边形的\textit{intriguing set}是一个点集，它能诱导强正则图的大小为2的公平划分。我们扩展的理论有趣的套广义四边形的班贝格，法律和Penttila部分四边形，这令人惊讶地提供了深入了解结构的半系统和其他有趣的套广义四边形。
英文摘要：
The point-line geometry known as a \textit{partial quadrangle} (introduced by Cameron in 1975) has the property that for every point/line non-incident pair $(P,\ell)$, there is at most one line through $P$ concurrent with $\ell$. So in particular, the well-studied objects known as \textit{generalised quadrangles} are each partial quadrangles. An \textit{intriguing set} of a generalised quadrangle is a set of points which induces an equitable partition of size two of the underlying strongly regular graph. We extend the theory of intriguing sets of generalised quadrangles by Bamberg, Law and Penttila to partial quadrangles, which surprisingly gives insight into the structure of hemisystems and other intriguing sets of generalised quadrangles.
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。
