Cutsets and anti-chains in linear lattices

Consider the poset, ordered by inclusion, of subspaces of a four-dimensional vector space over a field with 2 elements. We prove that, for this poset, any cutset (i.e., a collection of elements that intersects every maximal chain) contains a maximal anti-chain of the poset. In analogy with the same result by Duffus, Sands, and Winkler [D. Duffus, B. Sands, P. Winkler, Maximal chains and anti-chains in Boolean lattices, SIAM J. Discrete Math. 3 (2) (1990) 197-205] for the subset lattice, we conjecture that the above statement holds in any dimension and for any finite base field, and we prove some special cases to support the conjecture.     

用反链方法估计可分布尔函数的个数

用单层神经网络可表示的ｎ元布尔函数的计数问题一直未得到解决,本文利用反链工具给出这一计数的新的估计方法．