{"paper":{"title":"The hypergraph removal process","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Felix Joos, Marcus K\\\"uhn","submitted_at":"2024-12-19T16:50:52Z","abstract_excerpt":"Let $k\\geq 2$ and fix a $k$-uniform hypergraph $\\mathcal{F}$. Consider the random process that, starting from a $k$-uniform hypergraph $\\mathcal{H}$ on $n$ vertices, repeatedly deletes the edges of a copy of $\\mathcal{F}$ chosen uniformly at random and terminates when no copies of $\\mathcal{F}$ remain. Let $R(\\mathcal{H},\\mathcal{F})$ denote the number of edges that are left after termination. We show that $R(\\mathcal{H},\\mathcal{F})=n^{k-1/\\rho\\pm o(1)}$, where $\\rho:=(\\lvert E(\\mathcal{F})\\rvert-1)/(\\lvert V(\\mathcal{F})\\rvert -k)$, holds with high probability provided that $\\mathcal{F}$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15039","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/2412.15039/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"}