{"paper":{"title":"Polyhedral models for generalized associahedra via Coxeter elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Salvatore Stella","submitted_at":"2011-11-07T17:39:14Z","abstract_excerpt":"Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin and A. Zelevinsky associated to each finite type root system a simple convex polytope called \\emph{generalized associahedron}. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram.\n  In the first part of this paper, using the parametrization of cluster variables by their $g$-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1657","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"}