论文标题
在包装中的最大平行类中
On maximum parallel classes in packings
论文作者
论文摘要
整数$β（ρ，v，k）$被定义为任何$（v，k）$ - 包装中最大部分平行类（或ppc）中的最大块数。 Stinson介绍并研究了此问题，并研究了$ k = 3 $。在这里，我们主要考虑$ k = 4 $的情况，我们在$β（ρ，v，4）$上获得了一些上限和下限。我们还提供一些$（V，4）$的明确构造，包装最大PPC为给定尺寸$ρ$。对于$ρ$的少量值，构造包装的块数非常接近$β（ρ，v，4）$的上限。我们的一些方法扩展到$ k> 4 $的情况。
The integer $β(ρ, v, k)$ is defined to be the maximum number of blocks in any $(v, k)$-packing in which the maximum partial parallel class (or PPC) has size $ρ$. This problem was introduced and studied by Stinson for the case $k=3$. Here, we mainly consider the case $k = 4$ and we obtain some upper bounds and lower bounds on $β(ρ, v, 4)$. We also provide some explicit constructions of $(v,4)$-packings having a maximum PPC of a given size $ρ$. For small values of $ρ$, the number of blocks of the constructed packings are very close to the upper bounds on $β(ρ, v, 4)$. Some of our methods are extended to the cases $k > 4$.
