论文标题
在国旗传输不良2设计上
On flag-transitive imprimitive 2-designs
论文作者
论文摘要
1987年，休·戴维斯（Huw Davies）证明，对于旗帜传输点象征$ 2 $ - $（v，k，λ）$ design，块大小$ k $和数字$ v $ coint的功能都受$λ$的界限，但他并没有使这些界限。在本文中，我们得出了$λ$ bounding $ k $和$ v $的显式多项式功能。对于$λ\ leq 4 $，我们获得了“数字可行”参数集$ v，k，λ$的列表，以及不变点部分的零件数量和零件大小，以及非平凡的块零件交叉点的大小。此外，从这些参数集中，我们确定所有示例的示例少于$ 100 $。完全有11个这样的例子，对于这些设计之一，一种具有自动形态组$ {\ rm sym}（6）$的旗帜，点数较大的$ 2-（36,8,4）$设计，似乎先前在文献中没有构造。
In 1987, Huw Davies proved that, for a flag-transitive point-imprimitive $2$-$(v,k,λ)$ design, both the block-size $k$ and the number $v$ of points are bounded by functions of $λ$, but he did not make these bounds explicit. In this paper we derive explicit polynomial functions of $λ$ bounding $k$ and $v$. For $λ\leq 4$ we obtain a list of `numerically feasible' parameter sets $v, k, λ$ together with the number of parts and part-size of an invariant point-partition and the size of a nontrivial block-part intersection. Moreover from these parameter sets we determine all examples with fewer than $100$ points. There are exactly eleven such examples, and for one of these designs, a flag-regular, point-imprimitive $2-(36,8,4)$ design with automorphism group ${\rm Sym}(6)$, there seems to be no construction previously available in the literature.
