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arXiv · 2608.25453

Characterization of Maximal Left-Compressed Intersecting Families Generated by a Single Generator

Nguyen Trong Tuan
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Abstract

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 \(\mathcal{F}_G\).

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Nguyen Trong Tuan. 2026-08-26. Characterization of Maximal Left-Compressed Intersecting Families Generated by a Single Generator. https://arxiv.org/abs/2608.25453

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