A Combinatorial Theorem on Systems of Sets
A Combinatorial Theorem on Systems of Sets
复制标题
集合系统的组合定理
DOI：
10.1112/jlms/s1-43.1.204
复制
发表时间：
1968
影响因子：
1.2
通讯作者：
E. C. Milner
中科院分区：
文献类型：
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作者：
E. C. Milner
很容易看出，（2）和（3）给出了最好的可能结果。在[2]中也给出了n的上限估计，如果（Alt...，An）eS（k，k，m）和k（m+1），或者如果（Alt..，An）eS（k，I，m）和l^^（m+k），但在这些情况下的结果不是最好的。[3]和[4]中已建立了这类的其它结果，它们解决了[2]中的某些问题。在本文中，我们建立了Sperner结果（2）的如下推广.定理1. / /（A t，. . .，An）e S（k，< w，m）则
It is quite easy to see that (2) and (3) give best possible results. Upper estimates for n were also given in [2] if either (Alt..., An)eS(k, </, m) and /<^(m+l) or if (Alt..., An)eS(k, I, m) and l^^(m+k), but the results in these cases are not best possible. Other results of this kind have been established in [3] and [4] which settle certain conjectures made in [2]. In this note we establish the following generalisation of Sperner's result (2). THEOREM 1. / / (A t , . . . , A„) e S(k, < w, m) then