{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:58Z","timestamp":1759335838145,"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>We find, in the form of a continued fraction, the generating function for the number of $(132)$-avoiding permutations that have a given number of $(123)$ patterns, and show how to extend this to permutations that have exactly one $(132)$ pattern. We also find some properties of the continued fraction, which is similar to, though more general than, those that were studied by Ramanujan.<\/jats:p>","DOI":"10.37236\/1470","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:00:00Z","timestamp":1578708000000},"source":"Crossref","is-referenced-by-count":16,"title":["Permutation Patterns and Continued Fractions"],"prefix":"10.37236","volume":"6","author":[{"given":"Aaron","family":"Robertson","sequence":"first","affiliation":[]},{"given":"Herbert S.","family":"Wilf","sequence":"additional","affiliation":[]},{"given":"Doron","family":"Zeilberger","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,10,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r38\/appendix","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:32:10Z","timestamp":1579325530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,10,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1470","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,10,1]]},"article-number":"R38"}}