论文标题
与阿贝利安歌手族类型的部分几何形状有关的结果
Results on partial geometries with an abelian Singer group of rigid type
论文作者
论文摘要
如果所有$ s $的所有行均具有$ g $的微不足道稳定剂，则承认Abelian Singer Group $ G $的部分几何形状$ S $称为刚性类型。在本文中，我们表明，如果刚性类型的部分几何形状少于$ 1000000 $，则必须是van Lint-Schrijver几何形状，或者是具有1024或4096或194481点的假设几何形状，这提供了证据表明刚性类型的部分几何形状非常罕见。一路走来，我们还排除了一组无限的参数，这些参数最初对于构建刚性类型的部分几何形状似乎很有希望（因为它包含van Lint-Schrijver参数是其最小的情况，而其他情况之一我们不能排除作为该参数系列的第二个成员）。我们以这种类型的几何形状结束了论文。
A partial geometry $S$ admitting an abelian Singer group $G$ is called of rigid type if all lines of $S$ have a trivial stabilizer in $G$. In this paper, we show that if a partial geometry of rigid type has fewer than $1000000$ points it must be the Van Lint-Schrijver geometry or be a hypothetical geometry with 1024 or 4096 or 194481 points, which provides evidence that partial geometries of rigid type are very rare. Along the way we also exclude an infinite set of parameters that originally seemed very promising for the construction of partial geometries of rigid type (as it contains the Van Lint-Schrijver parameters as its smallest case and one of the other cases we cannot exclude as the second member of this parameter family). We end the paper with a conjecture on this type of geometries.
