{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T12:25:59Z","timestamp":1768566359710,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The minimum positive $\\ell$-degree $\\delta^+_{\\ell}(G)$ of a non-empty $k$-graph $G$ is the maximum $m$ such that every $\\ell$-subset of $V(G)$ is contained in either none or at least $m$ edges of~$G$; let $\\delta^+_{\\ell}(G):=0$ if $G$ has no edges. For a family $\\mathcal F$ of $k$-graphs, let $\\mathrm{co^{+}ex}_\\ell(n,\\mathcal F)$ be the maximum of $\\delta^+_{\\ell}(G)$ over all $\\mathcal F$-free $k$-graphs $G$ on $n$ vertices. We prove that the ratio $\\mathrm{co^{+}ex}_\\ell(n,\\mathcal F)\/{n-\\ell\\choose k-\\ell}$ tends to limit as $n\\to\\infty$, answering a question of Halfpap, Lemons and Palmer. Also, we show that the limit can be obtained as the value of a natural optimisation problem for $k$-hypergraphons; in fact, we give an alternative description of the set of possible accumulation points of almost extremal $k$-graphs.<\/jats:p>","DOI":"10.37236\/11912","type":"journal-article","created":{"date-parts":[[2023,8,24]],"date-time":"2023-08-24T19:30:54Z","timestamp":1692905454000},"source":"Crossref","is-referenced-by-count":6,"title":["On the Limit of the Positive $\\ell$-Degree Tur\u00e1n Problem"],"prefix":"10.37236","volume":"30","author":[{"given":"Oleg","family":"Pikhurko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2023,8,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p25\/8872","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p25\/8872","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,24]],"date-time":"2023-08-24T19:30:55Z","timestamp":1692905455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i3p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,25]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/11912","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,25]]},"article-number":"P3.25"}}