{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:08Z","timestamp":1753893788981,"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 give a parity reversing involution on noncrossing trees that leads to a combinatorial interpretation of a formula on noncrossing trees and symmetric ternary trees in answer to a problem proposed by Hough.  We use the representation of Panholzer and Prodinger for noncrossing trees and find a correspondence between a class of noncrossing trees, called proper noncrossing trees, and the set of symmetric ternary trees. The second result of this paper is a parity reversing involution on connected noncrossing graphs which leads to a relation between the number of noncrossing trees with $n$ edges and $k$ descents and the number of connected noncrossing graphs with $n+1$ vertices and $m$ edges.<\/jats:p>","DOI":"10.37236\/1150","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:59:01Z","timestamp":1578700741000},"source":"Crossref","is-referenced-by-count":5,"title":["Noncrossing Trees and  Noncrossing Graphs"],"prefix":"10.37236","volume":"13","author":[{"given":"William Y. C.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Sherry H. F.","family":"Yan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,8,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:09:51Z","timestamp":1579302591000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1n12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1150","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,8,14]]},"article-number":"N12"}}