{"paper":{"title":"The existence of designs via iterative absorption: hypergraph $F$-designs for arbitrary $F$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Allan Lo, Daniela K\\\"uhn, Deryk Osthus, Stefan Glock","submitted_at":"2016-11-21T15:12:33Z","abstract_excerpt":"We solve the existence problem for $F$-designs for arbitrary $r$-uniform hypergraphs~$F$. This implies that given any $r$-uniform hypergraph~$F$, the trivially necessary divisibility conditions are sufficient to guarantee a decomposition of any sufficiently large complete $r$-uniform hypergraph into edge-disjoint copies of~$F$, which answers a question asked e.g.~by Keevash. The graph case $r=2$ was proved by Wilson in 1975 and forms one of the cornerstones of design theory. The case when~$F$ is complete corresponds to the existence of block designs, a problem going back to the 19th century, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06827","kind":"arxiv","version":3},"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/1611.06827/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"}