{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852089,"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>Let ${\\cal CRF}_S$ denote the category of $S$-colored rooted forests, and H$_{{\\cal CRF}_S}$ denote its Ringel-Hall algebra as introduced by Kremnizer and Szczesny.  We construct a homomorphism from a $K^+_0({\\cal CRF}_S)$\u2013graded version of the Hopf algebra of noncommutative symmetric functions to H$_{{\\cal CRF}_S}$. Dualizing, we obtain a homomorphism from the Connes-Kreimer Hopf algebra to a $K^+_0({\\cal CRF}_S)$\u2013graded version of the algebra of quasisymmetric functions. This homomorphism is a refinement of one considered by W. Zhao.<\/jats:p>","DOI":"10.37236\/468","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:14:21Z","timestamp":1578716061000},"source":"Crossref","is-referenced-by-count":0,"title":["Colored Trees and Noncommutative Symmetric Functions"],"prefix":"10.37236","volume":"17","author":[{"given":"Matt","family":"Szczesny","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,4,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:56:54Z","timestamp":1579305414000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1n19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/468","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,4,5]]},"article-number":"N19"}}