{"paper":{"title":"Interval hypergraphic polytopes (or deformed associahedra), Tamari interval posets, and weeping willows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Sack, Eleni Tzanaki, F\\'elix G\\'elinas, Germain Poullot, Jose Bastidas, Vincent Pilaud","submitted_at":"2026-06-16T18:23:57Z","abstract_excerpt":"For a hypergraph $\\mathbb{H}$ on $[n]$, the hypergraphic polytope $\\triangle_{\\mathbb{H}}$ is the Minkowski sum of the standard simplices $\\triangle_H$ for all $H \\in \\mathbb{H}$. We focus here on interval hypergraphs, where all hyperedges are intervals of $[n]$. They are precisely the deformations of Loday's associahedron. Their vertex posets are Tamari interval posets, and we describe which Tamari interval poset appears as a vertex poset in which interval hypergraphic polytope. We also characterize the interval hypergraphs $\\mathbb{I}$ for which the hypergraphic polytope $\\triangle_\\mathbb{I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18376","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/2606.18376/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"}