{"paper":{"title":"Counting the number of elements in the mutation classes of \\tilde{A}_n-quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Christian Stump, Janine Bastian, Martin Rubey, Thomas Prellberg","submitted_at":"2009-06-02T14:11:37Z","abstract_excerpt":"In this article we prove explicit formulae for the number of non-isomorphic cluster-tilted algebras of type \\tilde{A}_n in the derived equivalence classes. In particular, we obtain the number of elements in the mutation classes of quivers of type \\tilde{A}_n. As a by-product, this provides an alternative proof for the number of quivers of Dynkin type D_n which was first determined by Buan and Torkildsen."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0487","kind":"arxiv","version":3},"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"}