{"paper":{"title":"Towards m-Cambrian Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henri M\\\"uhle, Myrto Kallipoliti","submitted_at":"2013-08-22T09:54:11Z","abstract_excerpt":"For positive integers $m$ and $k$, we introduce a family of lattices $\\mathcal{C}_{k}^{(m)}$ associated to the Cambrian lattice $\\mathcal{C}_{k}$ of the dihedral group $I_{2}(k)$. We show that $\\mathcal{C}_{k}^{(m)}$ satisfies some basic properties of a Fuss-Catalan generalization of $\\mathcal{C}_{k}$, namely that $\\mathcal{C}_{k}^{(1)}=\\mathcal{C}_{k}$ and $\\bigl\\lvert\\mathcal{C}_{k}^{(m)}\\bigr\\rvert=\\mbox{Cat}^{(m)}\\bigl(I_{2}(k)\\bigr)$. Subsequently, we prove some structural and topological properties of these lattices---namely that they are trim and EL-shellable---which were known for $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4813","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"}