论文标题
概括korchmáros-马佐科弧
Generalizing Korchmáros--Mazzocca arcs
论文作者
论文摘要
在本文中，我们概括了所谓的Korchmáros-Mazzocca Arcs，即$ Q+T $的点集，以$ 0、2 $或$ t $点相交的每条线在有限的订单$ Q $的有限投影平面中。对于$ t \ neq 2 $，这意味着点集的每个点都是事件发生的，正好一行满足$ t $点的点。 在$ \ mathrm {pg}（2，p^n）$中，我们将上述定义中的$ 2 $更改为任何整数$ m $，并描述所有示例当$ m $或$ t $不能被$ p $排除时。我们还研究了这些对象的mod $ p $变体，给出示例，在某些条件下，我们证明了核的存在。
In this paper, we generalize the so called Korchmáros--Mazzocca arcs, that is, point sets of size $q+t$ intersecting each line in $0, 2$ or $t$ points in a finite projective plane of order $q$. For $t\neq 2$, this means that each point of the point set is incident with exactly one line meeting the point set in $t$ points. In $\mathrm{PG}(2,p^n)$, we change $2$ in the definition above to any integer $m$ and describe all examples when $m$ or $t$ is not divisible by $p$. We also study mod $p$ variants of these objects, give examples and under some conditions we prove the existence of a nucleus.
