{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:15Z","timestamp":1753893795619,"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>Consider a random instance $I$ of $k$-SAT with $n$ variables and $m$ clauses. Suppose that $\\theta$, $c&gt;0$ are any fixed real numbers. Let $k=k(n)\\geq \\big(\\frac{1}{2}+\\theta\\big)\\log_{2}n$. We prove that \\begin{align}\\nonumber\\lim_{n\\rightarrow\\infty}Pr(I\\ \\mbox{is satifiable})=\\left\\{\\begin{array}{cc}1&amp;m\\leq\\big(1-\\frac{c}{\\sqrt{n}}\\big)2^{k}n\\ln 2 \\\\0&amp;m\\geq\\big(1+\\frac{c}{\\sqrt{n}}\\big)2^{k}n\\ln 2. \\\\\\end{array}\\right.\\end{align}<\/jats:p>","DOI":"10.37236\/1176","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:32:50Z","timestamp":1578713570000},"source":"Crossref","is-referenced-by-count":3,"title":["A Note on Random $k$-SAT for Moderately Growing $k$"],"prefix":"10.37236","volume":"19","author":[{"given":"Jun","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zongsheng","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,1,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:42:46Z","timestamp":1579300966000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/1176","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,1,21]]},"article-number":"P24"}}