{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:18Z","timestamp":1753893858180,"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>We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $\\mathcal{F}\\subseteq \\binom{[n]}{k}$.\u00a0Improving a bound of Balogh, Das, Delcourt, Liu and Sharifzadeh on $M(n,k)$, we determine the order of magnitude of $\\log M(n,k)$ by proving that for any fixed $k$, $M(n,k) =n^{\\Theta(\\binom{2k}{k})}$ holds. Our proof is based on Tuza's set pair approach.The main idea is to bound\u00a0the size of the largest possible point set of a cross-intersecting system. We also introduce and investigate some related functions and parameters.<\/jats:p>","DOI":"10.37236\/4955","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:20:53Z","timestamp":1578684053000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Number of Maximal Intersecting $k$-Uniform Families and Further Applications of Tuza's Set Pair Method"],"prefix":"10.37236","volume":"22","author":[{"given":"Zolt\u00e1n L\u00f3r\u00e1nt","family":"Nagy","sequence":"first","affiliation":[]},{"given":"Bal\u00e1zs","family":"Patk\u00f3s","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,3,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p83\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p83\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:23:08Z","timestamp":1579238588000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p83"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4955","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,3,30]]},"article-number":"P1.83"}}