{"paper":{"title":"On the Quiver Presentation of the Descent Algebra of the Symmetric Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.GR","authors_text":"G\\\"otz Pfeiffer, Marcus Bishop","submitted_at":"2012-06-01T23:19:33Z","abstract_excerpt":"We describe a presentation for the descent algebra of the symmetric group $\\sym{n}$ as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic image of an algebra of forests of binary trees which can be identified with a subspace of the free Lie algebra. In this setting, we provide a new short proof of the known fact that the quiver of the descent algebra of $\\sym{n}$ is given by restricted partition refinement. Moreover, we describe certain families of relations and conjecture that for fixed $n\\in\\mathbb{N}$, the finite set of relation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0327","kind":"arxiv","version":2},"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"}