{"paper":{"title":"Big Ramsey degrees of 3-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.LO"],"primary_cat":"math.CO","authors_text":"David Chodounsk\\'y, Jan Hubi\\v{c}ka, Lluis Vena, Martin Balko, Mat\\v{e}j Kone\\v{c}n\\'y","submitted_at":"2019-06-10T10:40:17Z","abstract_excerpt":"Given a countably infinite hypergraph $\\mathcal R$ and a finite hypergraph $\\mathcal A$, the big Ramsey degree of $\\mathcal A$ in $\\mathcal R$ is the least number $L$ such that, for every finite $k$ and every $k$-colouring of the embeddings of $\\mathcal A$ to $\\mathcal R$, there exists an embedding $f$ from $\\mathcal R$ to $\\mathcal R$ such that all the embeddings of $\\mathcal A$ to the image $f(\\mathcal R)$ have at most $L$ different colours.\n  We describe the big Ramsey degrees of the random countably infinite 3-uniform hypergraph, thereby solving a question of Sauer. We also give a new pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03888","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":""},"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"}