{"paper":{"title":"Multicolour containers and the entropy of decorated graph limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Uzzell, Johanna Str\\\"omberg, Kelly O'Connell, Victor Falgas-Ravry","submitted_at":"2016-07-27T15:35:32Z","abstract_excerpt":"In recent breakthrough results, Saxton--Thomason and Balogh--Morris--Samotij have developed powerful theories of hypergraph containers. These theories have led to a large number of new results on transference, and on counting and characterising typical graphs in hereditary properties. In a different direction, Hatami--Janson--Szegedy proved results on the entropy of graph limits which count and characterise graphs in dense hereditary properties.\n  In this paper, we make a threefold contribution to this area of research:\n  1) We generalise results of Saxton--Thomason to obtain container theorem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08152","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"}