有关相互非补的Sperner族的结论

摘要

With induction method the maximum bound of more than one Sperner families was investi-gated.Firstly,the case t=2 was proved in detail.Then,the case t was discussed through some special cases of pairwise uncomplemented Sperner familes. In the process, the Kruskal-Katona theorem was mainly used.Let Ai(i=1,…,2)be a Sperner family of subsets of [n].Ai and Ajare said to be pairwise uncomplemented,ifA∈Ai andAis not a member of Aj for anyi≠j.We prove that if A1,…At bet pairwise uncomplemented Sperner families of subsets of [n].%利用数学归纳研究1个以上Sperner集族的最大界问题。首先，对于t＝2的情况进行详细证明；然后，对于t个 pairwise uncomplemented Sperner集族进行分情况讨论。在此证明过程中，主要运用Kruskal-Ka-tona定理。设 Ai（i＝1，…，2））是由[n]形成的一列Sperner集族，如果对于任意的A∈ Ai和A不属于Aj ，则称Ai 和Aj 非补。