Improved Lower Bound for Frankl's UnionClosed Sets Conjecture
Abstract
We verify an explicit inequality conjectured recently by Gilmer, thus proving that for any nonempty unionclosed family $\mathcal F \subseteq 2^{[n]}$, some $i\in [n]$ is contained in at least $\frac{3\sqrt{5}}{2} \approx 0.38$ fraction of the sets in $\mathcal F$. One case, an explicit onevariable inequality, is checked by computer calculation.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.11731
 arXiv:
 arXiv:2211.11731
 Bibcode:
 2022arXiv221111731A
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 added a reference