{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:26Z","timestamp":1753893866648,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we confirm a special, remaining case of a conjecture of F\u00fcredi, Jiang, and Seiver, and determine an exact\u00a0formula for the Tur\u00e1n number $\\mathrm{ex}_3(n; P_3^3)$ of the 3-uniform linear path $P^3_3$ of length 3,\u00a0valid for all $n$. It coincides with the analogous formula for the 3-uniform\u00a0triangle $C^3_3$, obtained earlier by Frankl and F\u00fcredi for $n\\ge 75$ and Cs\u00e1k\u00e1ny and Kahn for\u00a0all $n$. In view of this coincidence, we also determine a `conditional' Tur\u00e1n number, defined as\u00a0the maximum number of edges in a $P^3_3$-free 3-uniform hypergraph on $n$ vertices which is not $C^3_3$-free.<\/jats:p>","DOI":"10.37236\/5320","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:10:24Z","timestamp":1578690624000},"source":"Crossref","is-referenced-by-count":5,"title":["Tur\u00e1n Numbers for  3-Uniform Linear Paths of Length 3"],"prefix":"10.37236","volume":"23","author":[{"given":"Eliza","family":"Jackowska","sequence":"first","affiliation":[]},{"given":"Joanna","family":"Polcyn","sequence":"additional","affiliation":[]},{"given":"Andrzej","family":"Ruci\u0144ski","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,5,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p30\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:28:34Z","timestamp":1579238914000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5320","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,5,13]]},"article-number":"P2.30"}}