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

Brice Huang; Mark Sellke; Ryan Alweiss

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2211.11731 v4 pith:DBNK35IL submitted 2022-11-21 math.CO

Ryan Alweiss , Brice Huang , Mark Sellke This is my paper · ORCID

classification math.CO

keywords explicitinequalitysetsunion-closedapproxboundcalculationcase

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

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

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Entropy approach for a generalization of Frankl's conjecture
math.CO 2024-12 accept novelty 6.0 of 10

A set family has an element in at least half its sets if and only if there exists an auxiliary family G satisfying an entropy inequality, giving a new equivalent form of Frankl's conjecture.

Pith tools