Work

Improved Lower Bound for Frankl’s Union-Closed Sets Conjecture

Year: 2024

Type: article

Abstract: We verify an explicit inequality conjectured in [Gilmer, 2022, arXiv:2211.09055], thus proving that for any nonempty union-closed family $\mathcal{F} \subseteq 2^{[n]}$, some $i\in [n]$ is contained in at least a $\frac{3-\sqrt{5}}{2} \approx 0.38$ fraction of the sets in $\mathcal{F} \$. One case, an explicit one-variable inequality, is checked by computer calculation.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12232

Authors: Ryan Alweiss, Brice Huang, Mark Sellke

Institutions: University of Cambridge, Massachusetts Institute of Technology, Harvard University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4402686388

FWCI: 3.255

Cites:

Cited by: 3

Related to: 10