Erds-Ko-Rado定理的一个新证明  

New Proof on Erds-Ko-Rado Theorem

作　　者：林庆泽[1] LIN Qingze(School of Physics and Electronic Engineering, Guangzhou University, Guaagzhou 510006, China)

机构地区：[1]广州大学物理与电子工程学院,广东广州510006

出　　处：《成都大学学报（自然科学版）》2016年第4期342-344,共3页Journal of Chengdu University（Natural Science Edition）

摘　　要：Erds-Ko-Rado定理是极值组合学里非常基础也非常重要的定理,它给出了自相交有限子集族里基数大小的上界的一个非常好的估计,在集合论和图论等相关领域有很多应用.证明方法很多,既有组合方面的,也有代数方面的.通过构建某些集合族间的2种单射以及一些相关的性质,诸如自相交性,给出了该定理的另一种证明方法.Erdos-Ko-Rado theorem is a very basic and very important theorem in the extremum combinatotics. It gives a very good estimate of the upper bound of the base size of serf-intersecting families of subsets and has been applied in many related fields of set theory and graph theory. There are many methods, consisting of combinatorics and algebras, to prove this theorem. In this paper,by constructing two kinds of injections between some families of subsets and by studying some related properties such as serf-intersections, the paper gives another proof on this theorem.

关 键 词：组合学 Erds-Ko-Rado定理 子集族 自相交性 

分 类 号：O157[理学—数学]