On Disjoint Chains of Subsets
On Disjoint Chains of Subsets
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关于不相交的子集链
DOI：
10.1006/jcta.2000.3148
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
D. Ron
中科院分区：
文献类型：
--
作者：
E. Lehman;D. Ron
我们证明了关于n的所有子集的偏序集按包含排序的下列定理。考虑n]的任意两个大小相等的子集族S和R，其中每个族内的所有子集都有相同数目的元素。设存在一个双射？：S？R使得对所有A？S都有A？F(A)，则存在包含S和R中所有子集的|S|不相交饱和链。
We prove the following theorem concerning the poset of all subsets of n] ordered by inclusion. Consider any two equal-size families of subsets of n], S and R, where within each family all subsets have the same number of elements. Suppose there exists a bijection ?:S?R such that A?f(A) for all A?S. Then there exist |S| disjoint saturated chains containing all the subsets in S and R.