{"paper":{"title":"C-sortable words as green mutation sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Yu Qiu","submitted_at":"2012-04-30T21:30:47Z","abstract_excerpt":"Let $Q$ be an acyclic quiver and $\\mathbf{s}$ be a sequence with elements in the vertex set $Q_0$. We describe an induced sequence of simple (backward) tilting in the bounded derived category $\\mathcal{D}(Q)$, starting from the standard heart $\\mathcal{H}_Q=\\operatorname{mod}\\mathbf{k}Q$ and ending at another heart $\\mathcal{H}_\\mathbf{s}$ in $\\mathcal{D}(Q)$. Then we show that $\\mathbf{s}$ is a green mutation sequence if and only if every heart in this simple tilting sequence is greater than or equal to $\\mathcal{H}_Q[-1]$; it is maximal if and only if $\\mathcal{H}_\\mathbf{s}=\\mathcal{H}_Q[-1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0034","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"}