{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T19:49:55Z","timestamp":1767988195977,"version":"3.49.0"},"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>For positive integers $n \\ge s &gt; r$, a Tur\u00e1n $(n,s,r)$-system is an $n$-vertex $r$-graph in which every set of $s$ vertices contains at least one edge. Let $T(n,s,r)$ denote the the minimum size of a Tur\u00e1n $(n,s,r)$-system.\r\nUpper bounds on $T(n,s,r)$ were established by Sidorenko for the case $s-r = \\Omega(r\/\\ln r)$, based on a construction of Frankl-R\u00f6dl, and by a number of authors in the case $s-r = O(1)$. Motivated by these results and recent work of the second author, we investigate in this note the intermediate regime where $s = s(r)$ satisfies both $s - r = \\Omega(1)$ and $s - r = O(r\/\\ln r)$, and establish upper bounds for $T(n,s,r)$ in this range as $r \\to \\infty$.<\/jats:p>","DOI":"10.37236\/14584","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:32:23Z","timestamp":1767969143000},"source":"Crossref","is-referenced-by-count":0,"title":["A Note on the Minimum Size of Tur\u00e1n Systems"],"prefix":"10.37236","volume":"33","author":[{"given":"Xizhi","family":"Liu","sequence":"first","affiliation":[]},{"given":"Oleg","family":"Pikhurko","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,1,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T14:32:23Z","timestamp":1767969143000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/14584","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,9]]},"article-number":"P1.4"}}