{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:29Z","timestamp":1753893809525,"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>To measure the difference between two intersecting families ${\\cal F},{\\cal G} \\subseteq 2^{[n]}$ we introduce the quantity $D({\\cal F} ,{\\cal G})=|\\{ (F,G):F \\in {\\cal F}, G \\in {\\cal G}, F\\cap G =\\emptyset \\}|$. We prove that if ${\\cal F}$ is $k$-uniform and ${\\cal G}$ is $l$-uniform, then for large enough $n$ and for any $i \\neq j$ ${\\cal F}_i=\\{F \\subseteq [n]: i \\in F, |F|=k \\}$ and ${\\cal F}_j=\\{F \\subseteq [n]: j \\in F, |F|=l\\}$ form an optimal pair of families (that is $D({\\cal F},{\\cal G}) \\leq D({\\cal F}_i,{\\cal F}_j)$ for all uniform and intersecting ${\\cal F}$ and ${\\cal G}$), while in the non-uniform case any pair of the form ${\\cal F}_i=\\{F \\subseteq [n]: i \\in F \\}$ and ${\\cal F}_j=\\{F \\subseteq [n]: j \\in F\\}$ is optimal for any $n$.<\/jats:p>","DOI":"10.37236\/1921","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:11:54Z","timestamp":1578719514000},"source":"Crossref","is-referenced-by-count":2,"title":["How Different Can Two Intersecting Families Be?"],"prefix":"10.37236","volume":"12","author":[{"given":"Bal\u00e1zs","family":"Patk\u00f3s","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,5,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:49:46Z","timestamp":1579322986000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1921","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,5,16]]},"article-number":"R24"}}