{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:20:27Z","timestamp":1759638027279,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Each length $k$ pattern occurs equally often in the set $S_n$ of\u00a0all permutations of length $n$, but the same is not true in\u00a0general for a proper subset of $S_n$. Mikl\u00f3s B\u00f3na recently\u00a0proved that if we consider the set of $n$-permutations avoiding\u00a0the pattern 132, all other non-monotone patterns of length 3 are\u00a0equally common. In this paper we focus on the set\u00a0$\\operatorname{Av}_n (123)$ of $n$-permutations avoiding $123$,\u00a0and give exact formulae for the occurrences of each length 3\u00a0pattern. While this set does not have the same symmetries as $\\operatorname{Av}_n (132)$, we find several similarities between\u00a0the two and prove that the number of 231 patterns is the same in\u00a0each.<\/jats:p>","DOI":"10.37236\/2515","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:23:39Z","timestamp":1578713019000},"source":"Crossref","is-referenced-by-count":6,"title":["Expected Patterns in Permutation Classes"],"prefix":"10.37236","volume":"19","author":[{"given":"Cheyne","family":"Homberger","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,10,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p43\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p43\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:30:35Z","timestamp":1579300235000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i3p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,4]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/2515","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,10,4]]},"article-number":"P43"}}