{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:26:17Z","timestamp":1759335977022,"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>Recently Han obtained a general formula for the weight function corresponding to the expansion  of a series in terms of hook lengths of binary trees. In this paper, we present weight function formulas for $k$-ary trees, plane trees, plane forests, labeled trees and forests. We also find appropriate generating functions which lead to unifications of the hook length formulas due to Du and Liu, Han, Gessel and Seo, and Postnikov.<\/jats:p>","DOI":"10.37236\/151","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:31:33Z","timestamp":1578717093000},"source":"Crossref","is-referenced-by-count":5,"title":["Hook Length Formulas for Trees by  Han's Expansion"],"prefix":"10.37236","volume":"16","author":[{"given":"William Y.C.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Oliver X.Q.","family":"Gao","sequence":"additional","affiliation":[]},{"given":"Peter L.","family":"Guo","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,5,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r62\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r62\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:55:16Z","timestamp":1579316116000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r62"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/151","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,5,15]]},"article-number":"R62"}}