{"paper":{"title":"Sublattices of associahedra and permutohedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Friedrich Wehrung (LMNO), Luigi Santocanale (LIF)","submitted_at":"2011-03-17T19:24:26Z","abstract_excerpt":"Gr\\\"atzer asked in 1971 for a characterization of sublattices of Tamari lattices (associahedra). A natural candidate was coined by McKenzie in 1972 with the notion of a bounded homomorphic image of a free lattice---in short, bounded lattice. Urquhart proved in 1978 that every associahedron is bounded (thus so are its sublattices). Geyer conjectured in 1994 that every finite bounded lattice embeds into some associahedron. We disprove Geyer's conjecture, by introducing an infinite collection of lattice-theoretical identities that hold in every associahedron, but not in every finite bounded latti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3488","kind":"arxiv","version":4},"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"}