{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:50Z","timestamp":1753893830737,"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 two hook length formulas for binary trees and asked for   combinatorial proofs. One of Han's formulas has been generalized to $k$-ary trees by Yang. Sagan has found a probabilistic proof of Yang's extension. We give combinatorial proofs of  Yang's formula for $k$-ary trees and the other formula of Han for binary trees. Our bijections are based on the structure of $k$-ary trees associated with staircase labelings.<\/jats:p>","DOI":"10.37236\/642","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:43:35Z","timestamp":1578714215000},"source":"Crossref","is-referenced-by-count":1,"title":["On Han's Hook Length Formulas for Trees"],"prefix":"10.37236","volume":"18","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":[[2011,7,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p155\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p155\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:07:35Z","timestamp":1579302455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p155"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/642","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,7,29]]},"article-number":"P155"}}