{"paper":{"title":"Two interacting Hopf algebras of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CO","authors_text":"Damien Calaque, Dominique Manchon, Kurusch Ebrahimi-Fard","submitted_at":"2008-06-13T12:53:55Z","abstract_excerpt":"Hopf algebra structures on rooted trees are by now a well-studied object, especially in the context of combinatorics. In this work we consider a Hopf algebra H by introducing a coproduct on a (commutative) algebra of rooted forests, considering each tree of the forest (which must contain at least one edge) as a Feynman-like graph without loops. The primitive part of the graded dual is endowed with a pre-Lie product defined in terms of insertion of a tree inside another. We establish a surprising link between the Hopf algebra H obtained this way and the well-known Connes-Kreimer Hopf algebra of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.2238","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}