{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:16:30Z","timestamp":1759335390247,"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 a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also expressed as a continued fraction. Among these problems is the enumeration of $(132)$-pattern avoiding permutations that have a given number of increasing patterns of length $k$. This extends and illuminates a result of Robertson, Wilf and Zeilberger for the case $k=3$.<\/jats:p>","DOI":"10.37236\/1523","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:03:23Z","timestamp":1578708203000},"source":"Crossref","is-referenced-by-count":6,"title":["Continued Fractions and Catalan Problems"],"prefix":"10.37236","volume":"7","author":[{"given":"Mahendra","family":"Jani","sequence":"first","affiliation":[]},{"given":"Robert G.","family":"Rieper","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,7,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r45\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r45\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:22:48Z","timestamp":1579324968000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,7,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1523","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,7,13]]},"article-number":"R45"}}