{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:11Z","timestamp":1753893851262,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $n, r$ and $\\ell$  be  distinct positive integers with  $r &lt;  \\ell\\leq n\/2$, and let  $X_1$ and $X_2$ be two disjoint sets with the same size $n$. Define $$\\mathcal{F}=\\left\\{A\\in \\binom{X}{r+\\ell}: \\mbox{$|A\\cap X_1|=r$ or $\\ell$}\\right\\},$$ where $X=X_1\\cup X_2$. In this paper, we prove that if $\\mathcal{S}$ is an intersecting family in $\\mathcal{F}$, then $|\\mathcal{S}|\\leq \\binom{n-1}{r-1}\\binom{n}{\\ell}+\\binom{n-1}{\\ell-1}\\binom{n}{r}$, and equality holds if and only if $\\mathcal{S}=\\{A\\in\\mathcal{F}: a\\in A\\}$ for some $a\\in X$.<\/jats:p>","DOI":"10.37236\/724","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:38:56Z","timestamp":1578713936000},"source":"Crossref","is-referenced-by-count":1,"title":["Intersecting Families in a Subset of Boolean Lattices"],"prefix":"10.37236","volume":"18","author":[{"given":"Jun","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huajun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,12,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p237\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p237\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:58:09Z","timestamp":1579301889000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p237"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/724","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,12,19]]},"article-number":"P237"}}