{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:43Z","timestamp":1753893823381,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $\\mathcal{B}(n)$ denote the collection of all set partitions\u00a0of $[n]$. Suppose $\\mathcal A_1,\\mathcal A_2\\subseteq \\mathcal{B}(n)$ are cross-intersecting i.e. for all $A_1\\in \\mathcal A_1$ and $A_2\\in \\mathcal A_2$, we have $A_1\\cap A_2\\neq\\varnothing$. It is proved that for sufficiently large $n$,\\[ \\vert \\mathcal A_1\\vert\\vert \\mathcal A_2\\vert\\leq B_{n-1}^2\\]where $B_{n}$ is the $n$-th Bell number. Moreover, equality holds if and only if $\\mathcal{A}_1=\\mathcal A_2$ and $\\mathcal A_1$ consists of all set partitions with a fixed singleton.<\/jats:p>","DOI":"10.37236\/2191","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:09:45Z","timestamp":1578712185000},"source":"Crossref","is-referenced-by-count":5,"title":["On Cross-Intersecting Families of Set Partitions"],"prefix":"10.37236","volume":"19","author":[{"given":"Cheng Yeaw","family":"Ku","sequence":"first","affiliation":[]},{"given":"Kok Bin","family":"Wong","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,12,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:21:11Z","timestamp":1579299671000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,31]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2191","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,12,31]]},"article-number":"P49"}}