{"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":1753893788959,"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>This note deals with a formula due to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symmetric group in some way. An elementary proof is provided as well as some immediate corollaries and applications, in particular a new application to the enumeration of $k$-decomposable trees.  A tree is called $k$-decomposable in this context if it has a spanning forest whose components are all of size $k$.<\/jats:p>","DOI":"10.37236\/1152","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:56:50Z","timestamp":1578718610000},"source":"Crossref","is-referenced-by-count":0,"title":["On an Identity for the Cycle Indices of Rooted Tree Automorphism Groups"],"prefix":"10.37236","volume":"13","author":[{"given":"Stephan G.","family":"Wagner","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,9,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1n14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:07:48Z","timestamp":1579320468000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1n14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,9,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1152","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,9,22]]},"article-number":"N14"}}