{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:13Z","timestamp":1753893793307,"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>For a set $L$ of positive proper fractions and a positive integer $r \\geq 2$, a fractional $r$-closed $L$-intersecting family is a collection $\\mathcal{F} \\subset \\mathcal{P}([n])$ with the property that for any $2 \\leq t \\leq r$ and $A_1, \\dotsc, A_t \\in \\mathcal{F}$ there exists $\\theta \\in L$ such that $\\lvert A_1 \\cap \\dotsb \\cap A_t \\rvert \\in \\{ \\theta \\lvert A_1 \\rvert, \\dotsc, \\theta \\lvert A_t \\rvert\\}$. In this paper we show that for $r \\geq 3$ and $L = \\{\\theta\\}$ any fractional $r$-closed $\\theta$-intersecting family has size at most linear in $n$, and this is best possible up to a constant factor. We also show that in the case $\\theta = 1\/2$ we have a tight upper bound of $\\lfloor \\frac{3n}{2} \\rfloor - 2$ and that a maximal $r$-closed $(1\/2)$-intersecting family is determined uniquely up to isomorphism.<\/jats:p>","DOI":"10.37236\/11651","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T02:47:33Z","timestamp":1701398853000},"source":"Crossref","is-referenced-by-count":0,"title":["On Hierarchically Closed Fractional Intersecting Families"],"prefix":"10.37236","volume":"30","author":[{"given":"Niranjan","family":"Balachandran","sequence":"first","affiliation":[]},{"given":"Srimanta","family":"Bhattacharya","sequence":"additional","affiliation":[]},{"given":"Krishn","family":"Kher","sequence":"additional","affiliation":[]},{"given":"Rogers","family":"Mathew","sequence":"additional","affiliation":[]},{"given":"Brahadeesh","family":"Sankarnarayanan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,12,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i4p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i4p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T02:47:34Z","timestamp":1701398854000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i4p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,1]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,10,6]]}},"URL":"https:\/\/doi.org\/10.37236\/11651","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,12,1]]},"article-number":"P4.37"}}