Characterization of Maximal Left-Compressed Intersecting Families Generated by a Single Generator
Nguyen Trong Tuan
Abstract
In this paper, we focus on left-compressed families \(F(G)\) generated by a family of sets \(G\). We establish a necessary and sufficient condition on \(G\) under which \(F(G)\) is intersecting. We then introduce a construction of maximal left-compressed intersecting families \(FG\) from a single generator by adding suitable sets not containing \(1\) to \(F(G)\). From this, we derive several estimates for the size of \(FG\).
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