{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:24:15Z","timestamp":1759335855081,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A family $\\mathcal F$ of $k$-element subsets of the $n$-element set $[n]$ is called \\emph{intersecting} if $F \\cap F'\\neq \\emptyset$ for all $F, F' \\in \\mathcal F$. In 1961 Erd\u0151s, Ko and Rado showed that $|\\mathcal F| \\leq {n - 1\\choose k - 1}$ if $n \\geq 2k$. Since then a large number of results\u0151 providing best possible upper bounds on $|\\mathcal F|$ under further restraints were proved. The paper of Li et al. is one of them. We consider the restricted universe $\\mathcal W = \\left\\{F \\in {[n]\\choose k}: |F \\cap [m]| \\geq \\ell \\right\\}$, $n \\geq 2k$, $m \\geq 2\\ell$ and determine $\\max |\\mathcal F|$ for intersecting families $\\mathcal F \\subset \\mathcal W$. Then we use this result to solve completely the problem considered by Li et al.<\/jats:p>","DOI":"10.37236\/8682","type":"journal-article","created":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T04:52:40Z","timestamp":1589518360000},"source":"Crossref","is-referenced-by-count":1,"title":["Erd\u0151s\u2013Ko\u2013Rado Theorem for a Restricted Universe"],"prefix":"10.37236","volume":"27","author":[{"given":"Peter","family":"Frankl","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,5,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p18\/8075","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p18\/8075","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T04:52:40Z","timestamp":1589518360000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,15]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/8682","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,5,15]]},"article-number":"P2.18"}}