{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:59Z","timestamp":1753893839253,"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>In the study of permutations, generalized patterns extend classical patterns by adding the requirement that certain adjacent integers in a pattern must be adjacent in the permutation.For any generalized pattern $\\pi_0^*$ of length $k$ with $1 \\leq b \\leq k$ blocks, we prove that for all $\\mu &gt; 0$, there exists $0 &lt; c =c(k, \\mu) &lt; 1$ so that whenever $n \\geq n_0(k, \\mu, c)$, all but $c^n n!$ many $\\pi \\in S_n$ admit $(1 \\pm \\mu) \\tfrac{1}{k!}\\tbinom{n}{b}$ occurrences of $\\pi_0^*$.\u00a0 Up to the choice of $c$, this result is best possible for all $\\pi_0^*$ with $k \\geq 2$.We also give a lower bound on avoidance of the generalized pattern $12$-$34$, which answers a question of S. Elizalde (2006).\u00a0<\/jats:p>","DOI":"10.37236\/2692","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:59:11Z","timestamp":1578711551000},"source":"Crossref","is-referenced-by-count":2,"title":["Generalized Pattern Frequency in Large Permutations"],"prefix":"10.37236","volume":"20","author":[{"given":"Joshua","family":"Cooper","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erik","family":"Lundberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brendan","family":"Nagle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,2,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:27:14Z","timestamp":1579260434000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2692","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,2,5]]},"article-number":"P28"}}