报告人：Ruizhong Wei (卫瑞中)教授 (Lakehead Univeristy)

报告时间：2023年11月9日，10:30-11:30

报告地点：逸夫楼235

报告摘要:

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 of k = 3. In this talk, we will discuss improvements of the bound of β(ρ, v, 3) and give some new constructions. Then, we will consider the cases of 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. Some interesting open problems will also be discussed.

邀请人：季利均、马欣荣