单个生成元生成的极大左压缩相交族的刻画
Characterization of Maximal Left-Compressed Intersecting Families Generated by a Single Generator
AI总结：
本文研究由集合族生成的左压缩相交族，建立其为相交族的充要条件，提出从单个生成元构造极大左压缩相交族的方法，并推导该族大小的相关估计值。
AI中文摘要：
本文聚焦由集合族\u2119生成的左压缩族\ud835\udf46(\u2119)，建立\ud835\udf46(\u2119)为相交族时\ud835\udc1d的充要条件；随后介绍从单个生成元构造极大左压缩相交族\ud835\udf46_G的方法，即向\ud835\udf46(\u2119)添加不含1的合适集合，并由此推导\ud835\udf46_G大小的若干估计值。
英文摘要：
In this paper, we focus on left-compressed families \(\mathcal{F}(\mathcal{G})\) generated by a family of sets \(\mathcal{G}\). We establish a necessary and sufficient condition on \(\mathcal{G}\) under which \(\mathcal{F}(\mathcal{G})\) is intersecting. We then introduce a construction of maximal left-compressed intersecting families \(\mathcal{F}_G\) from a single generator by adding suitable sets not containing \(1\) to \(F(G)\). From this, we derive several estimates for the size of \(\mathcal{F}_G\).
