On generating sets of left-compressed intersecting families
Combinatorics
2025-10-28 v3
Abstract
We construct a left-compressed family F(n, k, G) generated by a collection of generating sets G, and identify conditions on G under which F(n, k, G) is an intersecting family. From this, we obtain a convenient method to construct left-compressed intersecting families. After that, we provide some comparisons between the theorem of Bond and our result. Finally, we present some results on the generators of a maximal left-compressed intersecting family.
Keywords
Cite
@article{arxiv.2510.05666,
title = {On generating sets of left-compressed intersecting families},
author = {Tuan Nguyen and Thi Nguyen and Thu Tran},
journal= {arXiv preprint arXiv:2510.05666},
year = {2025}
}