{"paper":{"title":"An interactive version of the Lov\\'asz local lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"John Livieratos, Kostas I. Psaromiligkos, Lefteris Kirousis","submitted_at":"2017-08-13T18:56:53Z","abstract_excerpt":"Assume we are given (finitely many) mutually independent variables and (finitely many) \"undesirable\" events, each depending on a subset of the variables of at most $k$ elements, called the scope of the event. Assume that the probability of a variable belonging to the scope of an occurring event is bounded by $q$. We prove that if $ekq \\leq 1$ then there exists at least one assignment to the variables for which none of the events occurs. Examples are given where the criterion $ekq \\leq 1$ is applicable, whereas that of the classical version of the Lov\\'asz local lemma is not. The proof of the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03954","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":""},"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"}