{"paper":{"title":"Simplicial homeomorphs and trace-bounded hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bhargav Narayanan, Corrine Yap, Jason Long","submitted_at":"2020-11-16T18:45:25Z","abstract_excerpt":"Our first main result is a uniform bound, in every dimension $k \\in \\mathbb N$, on the topological Tur\\'an numbers of $k$-dimensional simplicial complexes: for each $k \\in \\mathbb N$, there is a $\\lambda_k \\ge k^{-2k^2}$ such that for any $k$-complex $\\mathcal{S}$, every $k$-complex on $n \\ge n_0(\\mathcal{S})$ vertices with at least $n^{k+1 - \\lambda_k}$ facets contains a homeomorphic copy of $\\mathcal{S}$. This was previously known only in dimensions one and two, both by highly dimension-specific arguments: the existence of $\\lambda_1$ is a result of Mader from 1967, and the existence of $\\la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.08167","kind":"arxiv","version":2},"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/2011.08167/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"}