{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:19:15Z","timestamp":1759335555226,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A descent  of a rooted tree with totally ordered vertices is a vertex that is greater than at least one of its children. A leaf  is a vertex with no children. We show that the number of forests of rooted trees on a given vertex set  with $i+1$ leaves and $j$ descents is equal to the number   with $j+1$ leaves and $i$ descents.  We do this by finding a functional equation for the   corresponding exponential generating function that shows that it is symmetric.<\/jats:p>","DOI":"10.37236\/1266","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:52:07Z","timestamp":1578707527000},"source":"Crossref","is-referenced-by-count":4,"title":["Counting Forests by Descents and Leaves"],"prefix":"10.37236","volume":"3","author":[{"given":"Ira M.","family":"Gessel","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1995,6,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i2r8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i2r8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T09:31:45Z","timestamp":1579339905000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i2r8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6,14]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[1996,1,24]]}},"URL":"https:\/\/doi.org\/10.37236\/1266","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1995,6,14]]},"article-number":"R8"}}