{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T12:42:16Z","timestamp":1778244136593,"version":"3.51.4"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.37236\/12232","type":"journal-article","created":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:33:39Z","timestamp":1726824819000},"source":"Crossref","is-referenced-by-count":1,"title":["Improved Lower Bound for Frankl\u2019s Union-Closed Sets Conjecture"],"prefix":"10.37236","volume":"31","author":[{"given":"Ryan","family":"Alweiss","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brice","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark","family":"Sellke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,9,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p35\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:33:39Z","timestamp":1726824819000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i3p35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,20]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/12232","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,20]]},"article-number":"P3.35"}}