论文标题
联盟封闭式猜想的笔记
Notes on the Union Closed Sets Conjecture
论文作者
论文摘要
联盟封闭式猜想指出，在每个有限的，非平凡的家族中，在占领工会下关闭的家族中至少有一半的家族集中都包含一个元素。我们研究了两个新方向关于猜想。首先，我们调查了工会封闭家庭中所有要素的频率，并提出了一个概括工会封闭式猜想的问题。其次，我们研究了相当于联盟封闭家庭的结构，并削弱了联合封闭场景的猜想。我们提出了一些有关工会封闭家庭和相关结构的新开放问题，并暗示了有关猜想的一些研究方向。
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to the conjecture. Firstly, we investigate the frequencies of all elements among a union closed family and pose a question generalizing the Union Closed Sets Conjecture. Secondly, we investigate structures equivalent to union closed families and obtain a weakening of the Union Closed Sets Conjecture. We pose some new open questions about union closed families and related structures and hint at some further directions of research regarding the conjecture.
