论文标题
旗帜传输，点象征对称$ 2 $ - $（v，k，λ）$设计，$ k>λ\ left（λ-3 \ right）/2 $
Flag-transitive, point-imprimitive symmetric $2$-$(v,k,λ)$ designs with $k>λ\left(λ-3 \right)/2$
论文作者
论文摘要
令$ \ Mathcal {d} = \ left（\ Mathcal {p}，\ Mathcal {b} \ right）$为对称$ 2 $ - $ - $（v，k，λ）$ design，承认承认具有flag flag flag trag tramistialitive point-simprimpphistimpphistimpphistimplyplyplyplymorphist $ g $ g $ g $ g $ g MATHCIAL a $ trivial a $ pright $ y-ftition $ g y-ftition $ y fortirial a $ c $。 praeger and khou \ cite {pz}已经表明，有一个常数$ k_ {0} $使得，对于每个$ b \ in \ nathcal {b} $和σ$中的$δ\ inσ$，大小为$ \ weft \ left \ welet \ welet b \ pert b \ pert b \capΔ\ right \ right \ right \ right \ right \ right $ 0 $ 0 $ 0 $ 0 $ 0 $ 0 $ k_ $ k_ {0 $ k_ {0。在本文中，我们表明，如果$ k>λ\左（λ-3 \右）/2 $和$ k_ {0} \ geq 3 $，$ \ nathcal {d} $是同构的，对已知的已知标志传播，点象征性的对称对称性$ 2 $ 2 $ -DESIGNS与PAMINETS $ 2 $ $ $（45）$（45）
Let $\mathcal{D}=\left(\mathcal{P},\mathcal{B} \right)$ be a symmetric $2$-$(v,k,λ)$ design admitting a flag-transitive, point-imprimitive automorphism group $G$ that leaves invariant a non-trivial partition $Σ$ of $\mathcal{P}$. Praeger and Zhou \cite{PZ} have shown that, there is a constant $k_{0}$ such that, for each $B \in \mathcal{B}$ and $Δ\in Σ$, the size of $\left\vert B \cap Δ\right \vert$ is either $0$ or $k_{0}$. In the present paper we show that, if $k>λ\left(λ-3 \right)/2$ and $k_{0} \geq 3$, $\mathcal{D}$ is isomorphic to one of the known flag-transitive, point-imprimitive symmetric $2$-designs with parameters $(45,12,3)$ or $(96,20,4)$.
