一类有限制条件的子集簇的模的上界

Upper Bound on the Size of Uncomplemented and Pairwise Incomparable Set Families

极值集合理论中的一类重要问题是研究有某种限制条件的子集簇的模的上界。利用数学归纳法加以数学实验的方法,证明了不自补的,两两不可比较的三个子集簇的模的严格上界。这个结果是A.J.W.Hilton的一个重要定理的推广。

In extremal set theory, people always focus on the size of some set families which have special properties. In this paper, we determine the upper bound of the sum of the size of, and, where, and are uncomplemented and pairwise incomparable set families. Our result is a generalization of a theorem due to A. J. W. Hilton.