{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821253,"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>Based on the classic bijective algorithm for trees due to Chen, we present a decomposition algorithm for noncrossing trees. This leads to a combinatorial interpretation of a formula on noncrossing trees of size $n$ with $k$ descents. We also derive the formula for noncrossing trees of size $n$ with $k$ descents and $i$ leaves, which is a refinement of the formula given by Flajolet and Noy. As an application of our algorithm, we answer a question proposed by Hough, which asks for a bijection between two classes of noncrossing trees with a given number of descents.<\/jats:p>","DOI":"10.37236\/3353","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:11:04Z","timestamp":1578705064000},"source":"Crossref","is-referenced-by-count":1,"title":["A Decomposition Algorithm for Noncrossing Trees"],"prefix":"10.37236","volume":"21","author":[{"given":"Lun","family":"Lv","sequence":"first","affiliation":[]},{"given":"Sabrina X.M.","family":"Pang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,1,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i1p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i1p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:06:53Z","timestamp":1579259213000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i1p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,1,13]]}},"URL":"https:\/\/doi.org\/10.37236\/3353","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,1,12]]},"article-number":"P1.5"}}