{"paper":{"title":"Natural endomorphisms of shuffle algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fr\\'ed\\'eric Patras (JAD), Lo\\\"ic Foissy (LM-Reims)","submitted_at":"2012-05-14T11:46:11Z","abstract_excerpt":"We focus in this text on the adaptation to the study of shuffles of the main combinatorial tool in the theory of free Lie algebras, namely the existence of a universal algebra of endomorphisms for tensor and other cocommutative Hopf algebras: the family of Solomon's descent algebras of type A. We show that there exists similarly a natural endomorphism algebra for commutative shuffle algebras, which is a natural extension of the Malvenuto-Reutenauer Hopf algebra of permutations, or algebra of free quasi-symmetric functions. We study this new algebra for its own, establish freeness properties, s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2986","kind":"arxiv","version":1},"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"}