{"paper":{"title":"Operahedron Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Sack, Colin Defant","submitted_at":"2024-02-20T05:01:48Z","abstract_excerpt":"Laplante-Anfossi associated to each rooted plane tree a polytope called an operahedron. He also defined a partial order on the vertex set of an operahedron and asked if the resulting poset is a lattice. We answer this question in the affirmative, motivating us to name Laplante-Anfossi's posets operahedron lattices. The operahedron lattice of a chain with $n+1$ vertices is isomorphic to the $n$-th Tamari lattice, while the operahedron lattice of a claw with $n+1$ vertices is isomorphic to $\\mathrm{Weak}(\\mathfrak S_n)$, the weak order on the symmetric group $\\mathfrak S_n$. We characterize semi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.12717","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.12717/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}