{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:44:15Z","timestamp":1774277055581,"version":"3.50.1"},"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, for a permutation $\\sigma \\in {\\cal S}_k$, the number $F(n,\\sigma)$ of permutations in ${\\cal S}_n$ which avoid $\\sigma$ as a subpattern.  The conjecture of Stanley and Wilf is that for every $\\sigma$  there is a constant $c(\\sigma) &lt;  \\infty$ such that for all $n$, $F(n,\\sigma) \\leq c(\\sigma)^n$.  All the recent work on this problem also mentions the \"stronger conjecture\" that for every $\\sigma$, the limit of $F(n,\\sigma)^{1\/n}$ exists and is finite. In this short note we prove that the two versions of the conjecture are equivalent, with a simple argument involving subadditivity We also discuss $n$-permutations, containing all $\\sigma \\in {\\cal S}_k$ as subpatterns.  We prove that this can be achieved with $n=k^2$, we conjecture that asymptotically $n \\sim (k\/e)^2$ is the best achievable, and we present Noga Alon's conjecture that  $n \\sim (k\/2)^2$ is the threshold for random permutations.<\/jats:p>","DOI":"10.37236\/1477","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:00:19Z","timestamp":1578708019000},"source":"Crossref","is-referenced-by-count":47,"title":["On the Stanley-Wilf Conjecture for the Number of Permutations Avoiding a Given Pattern"],"prefix":"10.37236","volume":"6","author":[{"given":"Richard","family":"Arratia","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,8,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1n1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1n1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:32:35Z","timestamp":1579325555000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1n1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,8,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1477","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,8,25]]},"article-number":"N1"}}